LMFDB - Embedded newform 840.2.cf.a.101.60

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(101,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 3, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.101"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.cf (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$128$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.60
Character	$\chi$	$=$	840.101
Dual form			840.2.cf.a.341.60

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.170119 + 1.40394i) q^{2} +(1.41157 - 1.00373i) q^{3} +(-1.94212 - 0.477674i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.16905 + 2.15252i) q^{6} +(2.47291 + 0.940605i) q^{7} +(1.00102 - 2.64537i) q^{8} +(0.985054 - 2.83367i) q^{9} +(0.554645 + 1.30091i) q^{10} +(1.85655 - 3.21564i) q^{11} +(-3.22089 + 1.27509i) q^{12} -6.09443 q^{13} +(-1.74124 + 3.31181i) q^{14} +(0.720590 - 1.57504i) q^{15} +(3.54366 + 1.85540i) q^{16} +(1.02488 - 1.77515i) q^{17} +(3.81073 + 1.86502i) q^{18} +(2.22451 + 3.85297i) q^{19} +(-1.92076 + 0.557382i) q^{20} +(4.43479 - 1.15440i) q^{21} +(4.19875 + 3.15354i) q^{22} +(5.38747 - 3.11046i) q^{23} +(-1.24223 - 4.73887i) q^{24} +(0.500000 - 0.866025i) q^{25} +(1.03678 - 8.55624i) q^{26} +(-1.45376 - 4.98864i) q^{27} +(-4.35338 - 3.00801i) q^{28} -1.24278 q^{29} +(2.08868 + 1.27961i) q^{30} +(-6.71818 - 3.87874i) q^{31} +(-3.20772 + 4.65946i) q^{32} +(-0.606984 - 6.40258i) q^{33} +(2.31786 + 1.74086i) q^{34} +(2.61190 - 0.421865i) q^{35} +(-3.26666 + 5.03279i) q^{36} +(-0.0470857 + 0.0271850i) q^{37} +(-5.78778 + 2.46763i) q^{38} +(-8.60271 + 6.11716i) q^{39} +(-0.455776 - 2.79146i) q^{40} +4.69122 q^{41} +(0.866272 + 6.42258i) q^{42} -6.68450i q^{43} +(-5.14167 + 5.35834i) q^{44} +(-0.563752 - 2.94655i) q^{45} +(3.45040 + 8.09286i) q^{46} +(6.22372 + 10.7798i) q^{47} +(6.86443 - 0.937847i) q^{48} +(5.23052 + 4.65206i) q^{49} +(1.13079 + 0.849299i) q^{50} +(-0.335077 - 3.53445i) q^{51} +(11.8361 + 2.91115i) q^{52} +(1.35995 - 2.35551i) q^{53} +(7.25109 - 1.19234i) q^{54} -3.71310i q^{55} +(4.96367 - 5.60018i) q^{56} +(7.00739 + 3.20592i) q^{57} +(0.211419 - 1.74479i) q^{58} +(-6.29130 - 3.63228i) q^{59} +(-2.15183 + 2.71471i) q^{60} +(4.32809 + 7.49648i) q^{61} +(6.58842 - 8.77210i) q^{62} +(5.10131 - 6.08084i) q^{63} +(-5.99593 - 5.29612i) q^{64} +(-5.27793 + 3.04721i) q^{65} +(9.09212 + 0.237025i) q^{66} +(-3.73488 - 2.15633i) q^{67} +(-2.83839 + 2.95799i) q^{68} +(4.48273 - 9.79819i) q^{69} +(0.147942 + 3.73873i) q^{70} +6.67812i q^{71} +(-6.51003 - 5.44238i) q^{72} +(8.02450 + 4.63295i) q^{73} +(-0.0301560 - 0.0707304i) q^{74} +(-0.163471 - 1.72432i) q^{75} +(-2.47981 - 8.54551i) q^{76} +(7.61573 - 6.20570i) q^{77} +(-7.12467 - 13.1184i) q^{78} +(6.87818 + 11.9134i) q^{79} +(3.99660 - 0.165004i) q^{80} +(-7.05934 - 5.58263i) q^{81} +(-0.798064 + 6.58621i) q^{82} +13.7830i q^{83} +(-9.16432 + 0.123598i) q^{84} -2.04977i q^{85} +(9.38466 + 1.13716i) q^{86} +(-1.75426 + 1.24741i) q^{87} +(-6.64811 - 8.13018i) q^{88} +(3.59457 + 6.22597i) q^{89} +(4.23270 - 0.290213i) q^{90} +(-15.0709 - 5.73245i) q^{91} +(-11.9489 + 3.46743i) q^{92} +(-13.3764 + 1.26812i) q^{93} +(-16.1930 + 6.90391i) q^{94} +(3.85297 + 2.22451i) q^{95} +(0.148918 + 9.79683i) q^{96} -10.4589i q^{97} +(-7.42104 + 6.55196i) q^{98} +(-7.28326 - 8.42843i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 30 q^{12} + 16 q^{16} - 10 q^{18} + 8 q^{22} + 128 q^{25} + 12 q^{28} - 40 q^{36} - 54 q^{42} + 16 q^{46} + 16 q^{49} + 36 q^{52} - 72 q^{54} - 16 q^{58} - 14 q^{60} + 80 q^{63} - 48 q^{64} - 60 q^{66}+ \cdots - 144 q^{96}+O(q^{100}) $ 256 * q + 30 * q^12 + 16 * q^16 - 10 * q^18 + 8 * q^22 + 128 * q^25 + 12 * q^28 - 40 * q^36 - 54 * q^42 + 16 * q^46 + 16 * q^49 + 36 * q^52 - 72 * q^54 - 16 * q^58 - 14 * q^60 + 80 * q^63 - 48 * q^64 - 60 * q^66 - 12 * q^70 - 50 * q^72 + 48 * q^73 - 16 * q^78 + 64 * q^79 - 8 * q^81 - 72 * q^82 - 56 * q^84 - 8 * q^88 - 72 * q^94 - 144 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.170119	+	1.40394i	−0.120292	+	0.992739i
$2$	−0.170119	+	1.40394i	−0.120292	+	0.992739i
$3$	1.41157	−	1.00373i	0.814970	−	0.579504i
$3$	1.41157	−	1.00373i	0.814970	−	0.579504i
$4$	−1.94212	−	0.477674i	−0.971060	−	0.238837i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$	1.16905	+	2.15252i	0.477261	+	0.878761i
$7$	2.47291	+	0.940605i	0.934670	+	0.355515i
$7$	2.47291	+	0.940605i	0.934670	+	0.355515i
$8$	1.00102	−	2.64537i	0.353913	−	0.935278i
$9$	0.985054	−	2.83367i	0.328351	−	0.944556i
$10$	0.554645	+	1.30091i	0.175394	+	0.411384i
$11$	1.85655	−	3.21564i	0.559772	−	0.969553i	−0.437744	−	0.899100i	$-0.644222\pi$
$11$	1.85655	−	3.21564i	0.559772	−	0.969553i	0.997515	−	0.0704529i	$-0.0224444\pi$
$12$	−3.22089	+	1.27509i	−0.929791	+	0.368088i
$13$	−6.09443			−1.69029			−0.845145	−	0.534537i	$-0.820486\pi$
$13$	−6.09443			−1.69029			−0.845145	+	0.534537i	$0.820486\pi$
$14$	−1.74124	+	3.31181i	−0.465367	+	0.885118i
$15$	0.720590	−	1.57504i	0.186055	−	0.406674i
$16$	3.54366	+	1.85540i	0.885914	+	0.463850i
$17$	1.02488	−	1.77515i	0.248571	−	0.430537i	−0.714559	−	0.699575i	$-0.753373\pi$
$17$	1.02488	−	1.77515i	0.248571	−	0.430537i	0.963129	+	0.269038i	$0.0867059\pi$
$18$	3.81073	+	1.86502i	0.898199	+	0.439589i
$19$	2.22451	+	3.85297i	0.510338	+	0.883931i	0.999928	+	0.0119787i	$0.00381305\pi$
$19$	2.22451	+	3.85297i	0.510338	+	0.883931i	−0.489590	+	0.871953i	$0.662854\pi$
$20$	−1.92076	+	0.557382i	−0.429495	+	0.124634i
$21$	4.43479	−	1.15440i	0.967751	−	0.251911i
$22$	4.19875	+	3.15354i	0.895176	+	0.672336i
$23$	5.38747	−	3.11046i	1.12337	−	0.648576i	0.181108	−	0.983463i	$-0.442032\pi$
$23$	5.38747	−	3.11046i	1.12337	−	0.648576i	0.942258	+	0.334888i	$0.108698\pi$
$24$	−1.24223	−	4.73887i	−0.253568	−	0.967317i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	1.03678	−	8.55624i	0.203328	−	1.67802i
$27$	−1.45376	−	4.98864i	−0.279777	−	0.960065i
$28$	−4.35338	−	3.00801i	−0.822711	−	0.568461i
$29$	−1.24278			−0.230778			−0.115389	−	0.993320i	$-0.536811\pi$
$29$	−1.24278			−0.230778			−0.115389	+	0.993320i	$0.536811\pi$
$30$	2.08868	+	1.27961i	0.381340	+	0.233624i
$31$	−6.71818	−	3.87874i	−1.20662	−	0.696643i	−0.244601	−	0.969624i	$-0.578657\pi$
$31$	−6.71818	−	3.87874i	−1.20662	−	0.696643i	−0.962019	+	0.272981i	$0.911990\pi$
$32$	−3.20772	+	4.65946i	−0.567050	+	0.823683i
$33$	−0.606984	−	6.40258i	−0.105662	−	1.11455i
$34$	2.31786	+	1.74086i	0.397510	+	0.298556i
$35$	2.61190	−	0.421865i	0.441492	−	0.0713081i
$36$	−3.26666	+	5.03279i	−0.544443	+	0.838798i
$37$	−0.0470857	+	0.0271850i	−0.00774085	+	0.00446918i	−0.503865	−	0.863782i	$-0.668089\pi$
$37$	−0.0470857	+	0.0271850i	−0.00774085	+	0.00446918i	0.496125	+	0.868251i	$0.334756\pi$
$38$	−5.78778	+	2.46763i	−0.938902	+	0.400302i
$39$	−8.60271	+	6.11716i	−1.37754	+	0.979529i
$40$	−0.455776	−	2.79146i	−0.0720645	−	0.441369i
$41$	4.69122			0.732646			0.366323	−	0.930488i	$-0.380617\pi$
$41$	4.69122			0.732646			0.366323	+	0.930488i	$0.380617\pi$
$42$	0.866272	+	6.42258i	0.133669	+	0.991026i
$43$		−	6.68450i		−	1.01938i	−0.860359	−	0.509688i	$-0.829761\pi$
$43$		−	6.68450i		−	1.01938i	0.860359	−	0.509688i	$-0.170239\pi$
$44$	−5.14167	+	5.35834i	−0.775137	+	0.807799i
$45$	−0.563752	−	2.94655i	−0.0840392	−	0.439246i
$46$	3.45040	+	8.09286i	0.508734	+	1.19323i
$47$	6.22372	+	10.7798i	0.907823	+	1.57240i	0.817082	+	0.576521i	$0.195590\pi$
$47$	6.22372	+	10.7798i	0.907823	+	1.57240i	0.0907407	+	0.995875i	$0.471077\pi$
$48$	6.86443	−	0.937847i	0.990796	−	0.135367i
$49$	5.23052	+	4.65206i	0.747218	+	0.664579i
$50$	1.13079	+	0.849299i	0.159918	+	0.120109i
$51$	−0.335077	−	3.53445i	−0.0469202	−	0.494922i
$52$	11.8361	+	2.91115i	1.64137	+	0.403704i
$53$	1.35995	−	2.35551i	0.186804	−	0.323554i	−0.757379	−	0.652976i	$-0.773520\pi$
$53$	1.35995	−	2.35551i	0.186804	−	0.323554i	0.944183	+	0.329422i	$0.106854\pi$
$54$	7.25109	−	1.19234i	0.986748	−	0.162257i
$55$		−	3.71310i		−	0.500675i
$56$	4.96367	−	5.60018i	0.663298	−	0.748355i
$57$	7.00739	+	3.20592i	0.928151	+	0.424635i
$58$	0.211419	−	1.74479i	0.0277607	−	0.229102i
$59$	−6.29130	−	3.63228i	−0.819058	−	0.472883i	0.0310337	−	0.999518i	$-0.490120\pi$
$59$	−6.29130	−	3.63228i	−0.819058	−	0.472883i	−0.850091	+	0.526635i	$0.823453\pi$
$60$	−2.15183	+	2.71471i	−0.277800	+	0.350467i
$61$	4.32809	+	7.49648i	0.554156	+	0.959826i	0.997969	+	0.0637065i	$0.0202921\pi$
$61$	4.32809	+	7.49648i	0.554156	+	0.959826i	−0.443813	+	0.896119i	$0.646375\pi$
$62$	6.58842	−	8.77210i	0.836731	−	1.11406i
$63$	5.10131	−	6.08084i	0.642704	−	0.766114i
$64$	−5.99593	−	5.29612i	−0.749491	−	0.662015i
$65$	−5.27793	+	3.04721i	−0.654647	+	0.377960i
$66$	9.09212	+	0.237025i	1.11916	+	0.0291757i
$67$	−3.73488	−	2.15633i	−0.456288	−	0.263438i	0.254194	−	0.967153i	$-0.418190\pi$
$67$	−3.73488	−	2.15633i	−0.456288	−	0.263438i	−0.710482	+	0.703715i	$0.751523\pi$
$68$	−2.83839	+	2.95799i	−0.344205	+	0.358709i
$69$	4.48273	−	9.79819i	0.539657	−	1.17956i
$70$	0.147942	+	3.73873i	0.0176824	+	0.446864i
$71$			6.67812i			0.792547i	0.918133	+	0.396273i	$0.129697\pi$
$71$			6.67812i			0.792547i	−0.918133	+	0.396273i	$0.870303\pi$
$72$	−6.51003	−	5.44238i	−0.767214	−	0.641391i
$73$	8.02450	+	4.63295i	0.939197	+	0.542246i	0.889708	−	0.456529i	$-0.150908\pi$
$73$	8.02450	+	4.63295i	0.939197	+	0.542246i	0.0494884	+	0.998775i	$0.484241\pi$
$74$	−0.0301560	−	0.0707304i	−0.00350557	−	0.00822225i
$75$	−0.163471	−	1.72432i	−0.0188760	−	0.199107i
$76$	−2.47981	−	8.54551i	−0.284453	−	0.980238i
$77$	7.61573	−	6.20570i	0.867893	−	0.707205i
$78$	−7.12467	−	13.1184i	−0.806710	−	1.48536i
$79$	6.87818	+	11.9134i	0.773856	+	1.34036i	0.935435	+	0.353498i	$0.115008\pi$
$79$	6.87818	+	11.9134i	0.773856	+	1.34036i	−0.161579	+	0.986860i	$0.551659\pi$
$80$	3.99660	−	0.165004i	0.446833	−	0.0184481i
$81$	−7.05934	−	5.58263i	−0.784371	−	0.620292i
$82$	−0.798064	+	6.58621i	−0.0881314	+	0.727325i
$83$			13.7830i			1.51288i	0.654061	+	0.756442i	$0.273064\pi$
$83$			13.7830i			1.51288i	−0.654061	+	0.756442i	$0.726936\pi$
$84$	−9.16432	+	0.123598i	−0.999909	+	0.0134856i
$85$		−	2.04977i		−	0.222328i
$86$	9.38466	+	1.13716i	1.01197	+	0.122623i
$87$	−1.75426	+	1.24741i	−0.188077	+	0.133737i
$88$	−6.64811	−	8.13018i	−0.708691	−	0.866680i
$89$	3.59457	+	6.22597i	0.381023	+	0.659952i	0.991209	−	0.132307i	$-0.0422384\pi$
$89$	3.59457	+	6.22597i	0.381023	+	0.659952i	−0.610186	+	0.792259i	$0.708905\pi$
$90$	4.23270	−	0.290213i	0.446166	−	0.0305911i
$91$	−15.0709	−	5.73245i	−1.57986	−	0.600924i
$92$	−11.9489	+	3.46743i	−1.24576	+	0.361504i
$93$	−13.3764	+	1.26812i	−1.38707	+	0.131498i
$94$	−16.1930	+	6.90391i	−1.67018	+	0.712084i
$95$	3.85297	+	2.22451i	0.395306	+	0.228230i
$96$	0.148918	+	9.79683i	0.0151989	+	0.999884i
$97$		−	10.4589i		−	1.06194i	−0.847392	−	0.530968i	$-0.821829\pi$
$97$		−	10.4589i		−	1.06194i	0.847392	−	0.530968i	$-0.178171\pi$
$98$	−7.42104	+	6.55196i	−0.749638	+	0.661848i
$99$	−7.28326	−	8.42843i	−0.731995	−	0.847089i
$100$	−1.38474	+	1.44309i	−0.138474	+	0.144309i
$101$	8.38258	+	4.83969i	0.834098	+	0.481567i	0.855254	−	0.518209i	$-0.173401\pi$
$101$	8.38258	+	4.83969i	0.834098	+	0.481567i	−0.0211557	+	0.999776i	$0.506735\pi$
$102$	5.01917	+	0.130846i	0.496972	+	0.0129557i
$103$	−8.88672	+	5.13075i	−0.875634	+	0.505548i	−0.869216	−	0.494432i	$-0.835376\pi$
$103$	−8.88672	+	5.13075i	−0.875634	+	0.505548i	−0.00641768	+	0.999979i	$0.502043\pi$
$104$	−6.10063	+	16.1220i	−0.598216	+	1.58089i
$105$	3.26344	−	3.21713i	0.318479	−	0.313960i
$106$	3.07565	+	2.31001i	0.298733	+	0.224368i
$107$	−7.03895	−	12.1918i	−0.680481	−	1.17863i	−0.974834	−	0.222930i	$-0.928438\pi$
$107$	−7.03895	−	12.1918i	−0.680481	−	1.17863i	0.294354	−	0.955696i	$-0.404896\pi$
$108$	0.440439	+	10.3830i	0.0423813	+	0.999102i
$109$	−8.58379	−	4.95586i	−0.822178	−	0.474685i	0.0289887	−	0.999580i	$-0.490771\pi$
$109$	−8.58379	−	4.95586i	−0.822178	−	0.474685i	−0.851167	+	0.524895i	$0.824105\pi$
$110$	5.21299	+	0.631668i	0.497039	+	0.0602272i
$111$	−0.0391784	+	0.0856348i	−0.00371865	+	0.00812810i
$112$	7.01793	+	7.92141i	0.663132	+	0.748503i
$113$		−	1.14945i		−	0.108131i	−0.998537	−	0.0540655i	$-0.982782\pi$
$113$		−	1.14945i		−	0.108131i	0.998537	−	0.0540655i	$-0.0172180\pi$
$114$	−5.69302	+	9.29260i	−0.533200	+	0.870332i
$115$	3.11046	−	5.38747i	0.290052	−	0.502385i
$116$	2.41362	+	0.593642i	0.224099	+	0.0551183i
$117$	−6.00334	+	17.2696i	−0.555009	+	1.59657i
$118$	6.16979	−	8.21472i	0.567975	−	0.756226i
$119$	4.20415	−	3.42577i	0.385394	−	0.314039i
$120$	−3.44523	−	3.48287i	−0.314505	−	0.317941i
$121$	−1.39357	−	2.41374i	−0.126688	−	0.219431i
$122$	−11.2609	+	4.80111i	−1.01952	+	0.434672i
$123$	6.62198	−	4.70872i	0.597084	−	0.424571i
$124$	11.1947	+	10.7421i	1.00532	+	0.964667i
$125$		−	1.00000i		−	0.0894427i
$126$	7.66934	+	8.19642i	0.683239	+	0.730195i
$127$	−8.96398			−0.795424			−0.397712	−	0.917510i	$-0.630196\pi$
$127$	−8.96398			−0.795424			−0.397712	+	0.917510i	$0.630196\pi$
$128$	8.45547	−	7.51698i	0.747365	−	0.664413i
$129$	−6.70943	−	9.43563i	−0.590732	−	0.830761i
$130$	−3.38025	−	7.92831i	−0.296467	−	0.695359i
$131$	12.9937	−	7.50189i	1.13526	−	0.655443i	0.190008	−	0.981783i	$-0.439149\pi$
$131$	12.9937	−	7.50189i	1.13526	−	0.655443i	0.945253	+	0.326340i	$0.105815\pi$
$132$	−1.87951	+	12.7245i	−0.163590	+	1.10753i
$133$	1.87689	+	11.6204i	0.162747	+	1.00762i
$134$	3.66275	−	4.87673i	0.316413	−	0.421285i
$135$	−3.75332	−	3.59341i	−0.323034	−	0.309272i
$136$	−3.66999	−	4.48815i	−0.314699	−	0.384855i
$137$	−9.81061	−	5.66416i	−0.838177	−	0.483922i	0.0184673	−	0.999829i	$-0.494121\pi$
$137$	−9.81061	−	5.66416i	−0.838177	−	0.483922i	−0.856644	+	0.515908i	$0.827455\pi$
$138$	12.9935	+	7.96036i	1.10608	+	0.677631i
$139$	−8.35456			−0.708625			−0.354312	−	0.935127i	$-0.615285\pi$
$139$	−8.35456			−0.708625			−0.354312	+	0.935127i	$0.615285\pi$
$140$	−5.27414	−	0.428326i	−0.445746	−	0.0362001i
$141$	19.6052	+	8.96950i	1.65106	+	0.755368i
$142$	−9.37571	−	1.13607i	−0.786792	−	0.0953370i
$143$	−11.3146	+	19.5975i	−0.946177	+	1.63883i
$144$	8.74828	−	8.21387i	0.729023	−	0.684489i
$145$	−1.07628	+	0.621388i	−0.0893799	+	0.0516035i
$146$	−7.86952	+	10.4778i	−0.651286	+	0.867149i
$147$	12.0527	+	1.31667i	0.994086	+	0.108597i
$148$	0.104432	−	0.0303048i	0.00858423	−	0.00249104i
$149$	−4.16644	−	7.21649i	−0.341328	−	0.591198i	0.643352	−	0.765571i	$-0.277543\pi$
$149$	−4.16644	−	7.21649i	−0.341328	−	0.591198i	−0.984680	+	0.174373i	$0.944210\pi$
$150$	2.44866	+	0.0638347i	0.199932	+	0.00521208i
$151$	−9.84977	+	17.0603i	−0.801563	+	1.38835i	0.117024	+	0.993129i	$0.462665\pi$
$151$	−9.84977	+	17.0603i	−0.801563	+	1.38835i	−0.918587	+	0.395219i	$0.870669\pi$
$152$	12.4193	−	2.02776i	1.00734	−	0.164473i
$153$	−4.02062	−	4.65279i	−0.325048	−	0.376156i
$154$	7.41688	+	11.7478i	0.597669	+	0.946662i
$155$	−7.75748			−0.623096
$156$	19.6295	−	7.77096i	1.57162	−	0.622175i
$157$	−7.84442	+	13.5869i	−0.626053	+	1.08436i	0.362283	+	0.932068i	$0.381997\pi$
$157$	−7.84442	+	13.5869i	−0.626053	+	1.08436i	−0.988336	+	0.152288i	$0.951336\pi$
$158$	−17.8958	+	7.62990i	−1.42371	+	0.607002i
$159$	−0.444626	−	4.68999i	−0.0352611	−	0.371940i
$160$	−0.448238	+	5.63907i	−0.0354363	+	0.445807i
$161$	16.2484	−	2.62439i	1.28056	−	0.206831i
$162$	9.03862	−	8.96121i	0.710141	−	0.704059i
$163$	−15.2175	+	8.78580i	−1.19192	+	0.688157i	−0.958742	−	0.284276i	$-0.908247\pi$
$163$	−15.2175	+	8.78580i	−1.19192	+	0.688157i	−0.233181	+	0.972433i	$0.574913\pi$
$164$	−9.11091	−	2.24087i	−0.711443	−	0.174983i
$165$	−3.72695	−	5.24130i	−0.290143	−	0.408035i
$166$	−19.3506	−	2.34475i	−1.50190	−	0.181988i
$167$	−13.3735			−1.03487			−0.517437	−	0.855721i	$-0.673114\pi$
$167$	−13.3735			−1.03487			−0.517437	+	0.855721i	$0.673114\pi$
$168$	1.38550	−	12.8872i	0.106893	−	0.994270i
$169$	24.1421			1.85708
$170$	2.87776	+	0.348703i	0.220714	+	0.0267443i
$171$	13.1093	−	2.50815i	1.00249	−	0.191803i
$172$	−3.19301	+	12.9821i	−0.243465	+	0.989875i
$173$	3.62060	−	2.09035i	0.275269	−	0.158927i	−0.356011	−	0.934482i	$-0.615863\pi$
$173$	3.62060	−	2.09035i	0.275269	−	0.158927i	0.631280	+	0.775555i	$0.282530\pi$
$174$	−1.45286	−	2.67510i	−0.110141	−	0.202799i
$175$	2.05104	−	1.67130i	0.155044	−	0.126338i
$176$	12.5453	−	7.95048i	0.945636	−	0.599290i
$177$	−12.5264	+	1.18755i	−0.941545	+	0.0892614i
$178$	−9.35242	+	3.98742i	−0.700994	+	0.298870i
$179$	−0.440634	+	0.763200i	−0.0329345	+	0.0570443i	−0.882023	−	0.471207i	$-0.843819\pi$
$179$	−0.440634	+	0.763200i	−0.0329345	+	0.0570443i	0.849088	+	0.528251i	$0.177152\pi$
$180$	−0.312618	+	5.99185i	−0.0233012	+	0.446606i
$181$	8.96185			0.666129			0.333065	−	0.942904i	$-0.391917\pi$
$181$	8.96185			0.666129			0.333065	+	0.942904i	$0.391917\pi$
$182$	10.6119	−	20.1836i	0.786606	−	1.49611i
$183$	13.6338	+	6.23756i	1.00784	+	0.461094i
$184$	−2.83535	−	17.3655i	−0.209024	−	1.28020i
$185$	−0.0271850	+	0.0470857i	−0.00199868	+	0.00346181i
$186$	0.495196	−	18.9954i	0.0363096	−	1.39281i
$187$	−3.80550	−	6.59131i	−0.278285	−	0.482005i
$188$	−6.93798	−	23.9086i	−0.506004	−	1.74371i
$189$	1.09732	−	13.7039i	0.0798185	−	0.996809i
$190$	−3.77855	+	5.03092i	−0.274125	+	0.364981i
$191$	2.66689	−	1.53973i	0.192969	−	0.111411i	−0.400403	−	0.916339i	$-0.631130\pi$
$191$	2.66689	−	1.53973i	0.192969	−	0.111411i	0.593372	+	0.804929i	$0.297796\pi$
$192$	−13.7795	−	1.45755i	−0.994452	−	0.105190i
$193$	−7.42255	+	12.8562i	−0.534287	+	0.925412i	0.464911	+	0.885357i	$0.346086\pi$
$193$	−7.42255	+	12.8562i	−0.534287	+	0.925412i	−0.999198	+	0.0400541i	$0.987247\pi$
$194$	14.6836	+	1.77924i	1.05422	+	0.127742i
$195$	−4.39158	+	9.59897i	−0.314488	+	0.687396i
$196$	−7.93613	−	11.5333i	−0.566867	−	0.823809i
$197$	−14.4448			−1.02915			−0.514574	−	0.857446i	$-0.672050\pi$
$197$	−14.4448			−1.02915			−0.514574	+	0.857446i	$0.672050\pi$
$198$	13.0721	−	8.79146i	0.928991	−	0.624782i
$199$	−15.8345	−	9.14203i	−1.12247	−	0.648061i	−0.180443	−	0.983585i	$-0.557753\pi$
$199$	−15.8345	−	9.14203i	−1.12247	−	0.648061i	−0.942032	+	0.335524i	$0.891087\pi$
$200$	−1.79045	−	2.18959i	−0.126604	−	0.154827i
$201$	−7.43642	+	0.704996i	−0.524524	+	0.0497266i
$202$	−8.22068	+	10.9454i	−0.578405	+	0.770113i
$203$	−3.07327	−	1.16896i	−0.215701	−	0.0820451i
$204$	−1.03756	+	7.02438i	−0.0726434	+	0.491805i
$205$	4.06272	−	2.34561i	0.283752	−	0.163825i
$206$	−5.69149	−	13.3493i	−0.396545	−	0.930089i
$207$	−3.50706	−	18.3303i	−0.243757	−	1.27404i
$208$	−21.5966	−	11.3076i	−1.49745	−	0.784041i
$209$	16.5197			1.14269
$210$	3.96151	+	5.12898i	0.273370	+	0.353934i
$211$			4.15688i			0.286171i	0.989710	+	0.143086i	$0.0457024\pi$
$211$			4.15688i			0.286171i	−0.989710	+	0.143086i	$0.954298\pi$
$212$	−3.76636	+	3.92506i	−0.258674	+	0.269574i
$213$	6.70303	+	9.42663i	0.459284	+	0.645902i
$214$	18.3141	−	7.80823i	1.25192	−	0.533760i
$215$	−3.34225	−	5.78894i	−0.227939	−	0.394803i
$216$	−14.6520	−	1.14798i	−0.996945	−	0.0781104i
$217$	−12.9651	−	15.9109i	−0.880125	−	1.08010i
$218$	8.41801	−	11.2081i	0.570140	−	0.759107i
$219$	15.9774	−	1.51470i	1.07965	−	0.102354i
$220$	−1.77365	+	7.21129i	−0.119580	+	0.486185i
$221$	−6.24608	+	10.8185i	−0.420157	+	0.727732i
$222$	−0.113562	−	0.0695724i	−0.00762175	−	0.00466939i
$223$		−	23.3392i		−	1.56291i	−0.623962	−	0.781455i	$-0.714478\pi$
$223$		−	23.3392i		−	1.56291i	0.623962	−	0.781455i	$-0.285522\pi$
$224$	−12.3151	+	8.50520i	−0.822837	+	0.568277i
$225$	−1.96150	−	2.26992i	−0.130767	−	0.151328i
$226$	1.61376	+	0.195542i	0.107346	+	0.0130073i
$227$	−9.87389	−	5.70069i	−0.655353	−	0.378368i	0.135151	−	0.990825i	$-0.456848\pi$
$227$	−9.87389	−	5.70069i	−0.655353	−	0.378368i	−0.790504	+	0.612457i	$0.790181\pi$
$228$	−12.0778	−	9.57353i	−0.799872	−	0.634022i
$229$	6.03573	+	10.4542i	0.398852	+	0.690832i	0.993585	−	0.113092i	$-0.0360754\pi$
$229$	6.03573	+	10.4542i	0.398852	+	0.690832i	−0.594733	+	0.803924i	$0.702742\pi$
$230$	7.03457	+	5.28342i	0.463846	+	0.348378i
$231$	4.52128	−	16.4039i	0.297479	−	1.07930i
$232$	−1.24404	+	3.28760i	−0.0816753	+	0.215841i
$233$	−7.49815	+	4.32906i	−0.491220	+	0.283606i	−0.725080	−	0.688664i	$-0.758197\pi$
$233$	−7.49815	+	4.32906i	−0.491220	+	0.283606i	0.233860	+	0.972270i	$0.424864\pi$
$234$	−23.2243	−	11.3662i	−1.51822	−	0.743034i
$235$	10.7798	+	6.22372i	0.703197	+	0.405991i
$236$	10.4834	+	10.0595i	0.682412	+	0.654819i
$237$	21.6668	+	9.91270i	1.40741	+	0.643899i
$238$	4.09438	+	6.48518i	0.265399	+	0.420372i
$239$		−	6.96486i		−	0.450519i	−0.974299	−	0.225260i	$-0.927677\pi$
$239$		−	6.96486i		−	0.450519i	0.974299	−	0.225260i	$-0.0723230\pi$
$240$	5.47585	−	4.24442i	0.353465	−	0.273976i
$241$	12.7589	+	7.36635i	0.821873	+	0.474509i	0.851062	−	0.525065i	$-0.175959\pi$
$241$	12.7589	+	7.36635i	0.821873	+	0.474509i	−0.0291890	+	0.999574i	$0.509292\pi$
$242$	3.62583	−	1.54588i	0.233077	−	0.0993727i
$243$	−15.5682	−	0.794597i	−0.998700	−	0.0509734i
$244$	−4.82480	−	16.6265i	−0.308876	−	1.06440i
$245$	6.85579	+	1.41354i	0.438001	+	0.0903076i
$246$	5.48425	+	10.0979i	0.349663	+	0.643821i
$247$	−13.5571	−	23.4816i	−0.862620	−	1.49410i
$248$	−16.9857	+	13.8894i	−1.07859	+	0.881975i
$249$	13.8344	+	19.4557i	0.876722	+	1.23295i
$250$	1.40394	+	0.170119i	0.0887932	+	0.0107592i
$251$			18.1064i			1.14286i	0.820650	+	0.571432i	$0.193612\pi$
$251$			18.1064i			1.14286i	−0.820650	+	0.571432i	$0.806388\pi$
$252$	−12.8120	+	9.37296i	−0.807081	+	0.590441i
$253$		−	23.0989i		−	1.45222i
$254$	1.52494	−	12.5849i	0.0956832	−	0.789648i
$255$	−2.05741	−	2.89339i	−0.128840	−	0.181191i
$256$	9.11498	+	13.1498i	0.569687	+	0.821862i
$257$	−0.111463	−	0.193060i	−0.00695287	−	0.0120427i	0.862528	−	0.506009i	$-0.168880\pi$
$257$	−0.111463	−	0.193060i	−0.00695287	−	0.0120427i	−0.869481	+	0.493967i	$0.835547\pi$
$258$	14.3885	−	7.81449i	0.895788	−	0.486509i
$259$	−0.142009	+	0.0229368i	−0.00882401	+	0.00142522i
$260$	11.7059	−	3.39692i	0.725972	−	0.210668i
$261$	−1.22420	+	3.52161i	−0.0757762	+	0.217982i
$262$	8.32177	+	19.5186i	0.514121	+	1.20586i
$263$	2.77290	+	1.60093i	0.170984	+	0.0987178i	0.583050	−	0.812436i	$-0.301859\pi$
$263$	2.77290	+	1.60093i	0.170984	+	0.0987178i	−0.412066	+	0.911154i	$0.635193\pi$
$264$	−17.5448	−	4.80340i	−1.07981	−	0.295629i
$265$		−	2.71991i		−	0.167083i
$266$	−16.6337	+	0.658196i	−1.01988	+	0.0403566i
$267$	11.3232	+	5.18042i	0.692967	+	0.317036i
$268$	6.22356	+	5.97191i	0.380164	+	0.364793i
$269$	16.6455	+	9.61028i	1.01489	+	0.585949i	0.912621	−	0.408807i	$-0.134055\pi$
$269$	16.6455	+	9.61028i	1.01489	+	0.585949i	0.102273	+	0.994756i	$0.467388\pi$
$270$	5.68346	−	4.65815i	0.345884	−	0.283486i
$271$	1.19595	−	0.690483i	0.0726489	−	0.0419439i	−0.463236	−	0.886235i	$-0.653312\pi$
$271$	1.19595	−	0.690483i	0.0726489	−	0.0419439i	0.535884	+	0.844291i	$0.319978\pi$
$272$	6.92544	−	4.38895i	0.419917	−	0.266119i
$273$	−27.0275	+	7.03540i	−1.63578	+	0.425802i
$274$	9.62113	−	12.8100i	0.581234	−	0.773879i
$275$	−1.85655	−	3.21564i	−0.111954	−	0.193911i
$276$	−13.3863	+	16.8880i	−0.805763	+	1.01654i
$277$	6.38282	+	3.68512i	0.383507	+	0.221418i	0.679343	−	0.733821i	$-0.262265\pi$
$277$	6.38282	+	3.68512i	0.383507	+	0.221418i	−0.295836	+	0.955239i	$0.595598\pi$
$278$	1.42127	−	11.7293i	0.0852419	−	0.703479i
$279$	−17.6088	+	15.2163i	−1.05421	+	0.910977i
$280$	1.49857	−	7.33173i	0.0895569	−	0.438155i
$281$		−	4.85308i		−	0.289511i	−0.989467	−	0.144755i	$-0.953761\pi$
$281$		−	4.85308i		−	0.289511i	0.989467	−	0.144755i	$-0.0462395\pi$
$282$	−15.9279	+	25.9988i	−0.948492	+	1.54820i
$283$	6.01870	−	10.4247i	0.357775	−	0.619684i	−0.629814	−	0.776746i	$-0.716869\pi$
$283$	6.01870	−	10.4247i	0.357775	−	0.619684i	0.987589	+	0.157062i	$0.0502023\pi$
$284$	3.18996	−	12.9697i	0.189290	−	0.769610i
$285$	7.67154	−	0.727286i	0.454423	−	0.0430807i
$286$	−25.5890	−	19.2190i	−1.51311	−	1.13644i
$287$	11.6009	+	4.41259i	0.684782	+	0.260467i
$288$	10.0436	+	13.6794i	0.591823	+	0.806068i
$289$	6.39923	+	11.0838i	0.376425	+	0.651988i
$290$	−0.689300	−	1.61674i	−0.0404771	−	0.0949383i
$291$	−10.4979	−	14.7634i	−0.615395	−	0.865445i
$292$	−13.3715	−	12.8308i	−0.782508	−	0.750868i
$293$			23.0767i			1.34816i	0.738660	+	0.674078i	$0.235459\pi$
$293$			23.0767i			1.34816i	−0.738660	+	0.674078i	$0.764541\pi$
$294$	−3.89891	+	16.6973i	−0.227389	+	0.973804i
$295$	−7.26457			−0.422960
$296$	0.0247805	+	0.151772i	0.00144034	+	0.00882155i
$297$	−18.7407	−	4.58689i	−1.08744	−	0.266158i
$298$	10.8403	−	4.62179i	0.627964	−	0.267733i
$299$	−32.8336	+	18.9565i	−1.89881	+	1.09628i
$300$	−0.506182	+	3.42692i	−0.0292245	+	0.197853i
$301$	6.28747	−	16.5301i	0.362404	−	0.952781i
$302$	−22.2761	−	16.7308i	−1.28184	−	0.962750i
$303$	16.6903	−	1.58230i	0.958834	−	0.0909005i
$304$	0.734109	+	17.7809i	0.0421040	+	1.01981i
$305$	7.49648	+	4.32809i	0.429247	+	0.247826i
$306$	7.21624	−	4.85320i	0.412525	−	0.277439i
$307$	−7.15756			−0.408503			−0.204252	−	0.978918i	$-0.565476\pi$
$307$	−7.15756			−0.408503			−0.204252	+	0.978918i	$0.565476\pi$
$308$	−17.7550	+	8.41437i	−1.01168	+	0.479453i
$309$	−7.39433	+	16.1623i	−0.420649	+	0.919439i
$310$	1.31969	−	10.8911i	0.0749535	−	0.618572i
$311$	11.6494	−	20.1774i	0.660579	−	1.14416i	−0.319885	−	0.947456i	$-0.603644\pi$
$311$	11.6494	−	20.1774i	0.660579	−	1.14416i	0.980464	−	0.196699i	$-0.0630223\pi$
$312$	7.57066	+	28.8807i	0.428604	+	1.63505i
$313$	−2.53839	+	1.46554i	−0.143478	+	0.0828371i	−0.570021	−	0.821630i	$-0.693065\pi$
$313$	−2.53839	+	1.46554i	−0.143478	+	0.0828371i	0.426542	+	0.904468i	$0.359731\pi$
$314$	−17.7408	−	13.3245i	−1.00117	−	0.751946i
$315$	1.37744	−	7.81682i	0.0776099	−	0.440428i
$316$	−7.66755	−	26.4227i	−0.431333	−	1.48639i
$317$	−7.73492	−	13.3973i	−0.434436	−	0.752466i	0.562813	−	0.826584i	$-0.309719\pi$
$317$	−7.73492	−	13.3973i	−0.434436	−	0.752466i	−0.997249	+	0.0741183i	$0.976386\pi$
$318$	6.66012	+	0.173624i	0.373481	+	0.00973637i
$319$	−2.30728	+	3.99632i	−0.129183	+	0.223751i
$320$	−7.84068	−	1.58861i	−0.438308	−	0.0888061i
$321$	−22.1732	−	10.1444i	−1.23759	−	0.566204i
$322$	0.920332	+	23.2583i	0.0512881	+	1.29614i
$323$	9.11946			0.507420
$324$	11.0434	+	14.2142i	0.613522	+	0.789677i
$325$	−3.04721	+	5.27793i	−0.169029	+	0.292767i
$326$	−9.74601	−	22.8591i	−0.539781	−	1.26605i
$327$	−17.0910	+	1.62028i	−0.945132	+	0.0896015i
$328$	4.69600	−	12.4100i	0.259293	−	0.685227i
$329$	5.25114	+	32.5115i	0.289504	+	1.79242i
$330$	7.99252	−	4.34079i	0.439974	−	0.238953i
$331$	5.85964	−	3.38307i	0.322075	−	0.185950i	−0.330242	−	0.943896i	$-0.607130\pi$
$331$	5.85964	−	3.38307i	0.322075	−	0.185950i	0.652317	+	0.757946i	$0.273797\pi$
$332$	6.58380	−	26.7683i	0.361333	−	1.46910i
$333$	0.0306512	+	0.160204i	0.00167967	+	0.00877912i
$334$	2.27508	−	18.7757i	0.124487	−	1.02736i
$335$	−4.31267			−0.235626
$336$	17.8572	+	4.13751i	0.974192	+	0.225720i
$337$	30.5079			1.66187			0.830935	−	0.556369i	$-0.187806\pi$
$337$	30.5079			1.66187			0.830935	+	0.556369i	$0.187806\pi$
$338$	−4.10701	+	33.8941i	−0.223392	+	1.84360i
$339$	−1.15373	−	1.62252i	−0.0626623	−	0.0881235i
$340$	−0.979120	+	3.98089i	−0.0531002	+	0.215894i
$341$	−24.9453	+	14.4022i	−1.35086	+	0.779921i
$342$	1.29116	+	18.8314i	0.0698182	+	1.01829i
$343$	8.55884	+	16.4240i	0.462134	+	0.886810i
$344$	−17.6829	−	6.69130i	−0.953400	−	0.360771i
$345$	−1.01694	−	10.7269i	−0.0547502	−	0.577514i
$346$	2.31881	+	5.43873i	0.124660	+	0.292388i
$347$	−14.6599	+	25.3916i	−0.786983	+	1.36309i	0.140825	+	0.990035i	$0.455025\pi$
$347$	−14.6599	+	25.3916i	−0.786983	+	1.36309i	−0.927807	+	0.373059i	$0.878309\pi$
$348$	4.00285	−	1.58466i	0.214575	−	0.0849465i
$349$	3.82060			0.204512			0.102256	−	0.994758i	$-0.467394\pi$
$349$	3.82060			0.204512			0.102256	+	0.994758i	$0.467394\pi$
$350$	1.99749	+	3.16387i	0.106770	+	0.169116i
$351$	8.85986	+	30.4029i	0.472905	+	1.62279i
$352$	9.02785	+	18.9654i	0.481186	+	1.01086i
$353$	−2.49574	+	4.32274i	−0.132835	+	0.230076i	−0.924768	−	0.380531i	$-0.875741\pi$
$353$	−2.49574	+	4.32274i	−0.132835	+	0.230076i	0.791934	+	0.610607i	$0.209075\pi$
$354$	0.463731	−	17.7884i	0.0246470	−	0.945445i
$355$	3.33906	+	5.78342i	0.177219	+	0.306952i
$356$	−4.00709	−	13.8086i	−0.212375	−	0.731855i
$357$	2.49591	−	9.05554i	0.132098	−	0.479270i
$358$	−0.996531	−	0.748460i	−0.0526683	−	0.0395573i
$359$	16.3630	−	9.44720i	0.863608	−	0.498604i	−0.00161106	−	0.999999i	$-0.500513\pi$
$359$	16.3630	−	9.44720i	0.863608	−	0.498604i	0.865219	+	0.501395i	$0.167179\pi$
$360$	−8.35904	−	1.45822i	−0.440560	−	0.0768551i
$361$	−0.396906	+	0.687462i	−0.0208898	+	0.0361822i
$362$	−1.52458	+	12.5819i	−0.0801300	+	0.661292i
$363$	−4.38986	−	2.00839i	−0.230408	−	0.105413i
$364$	26.5313	+	18.3321i	1.39062	+	0.960863i
$365$	9.26590			0.484999
$366$	−11.0766	+	18.0800i	−0.578981	+	0.945058i
$367$	0.575814	+	0.332446i	0.0300572	+	0.0173536i	0.514953	−	0.857218i	$-0.327809\pi$
$367$	0.575814	+	0.332446i	0.0300572	+	0.0173536i	−0.484896	+	0.874572i	$0.661143\pi$
$368$	24.8625	−	1.02648i	1.29605	−	0.0535089i
$369$	4.62110	−	13.2934i	0.240565	−	0.692025i
$370$	−0.0614811	−	0.0461763i	−0.00319625	−	0.00240059i
$371$	5.57864	−	4.54577i	0.289629	−	0.236005i
$372$	26.5843	+	3.92670i	1.37833	+	0.203590i
$373$	11.4621	−	6.61763i	0.593484	−	0.342648i	−0.172990	−	0.984924i	$-0.555343\pi$
$373$	11.4621	−	6.61763i	0.593484	−	0.342648i	0.766474	+	0.642275i	$0.222009\pi$
$374$	9.90122	−	4.22140i	0.511980	−	0.218283i
$375$	−1.00373	−	1.41157i	−0.0518324	−	0.0728931i
$376$	34.7466	−	5.67325i	1.79192	−	0.292575i
$377$	7.57401			0.390082
$378$	19.0528	+	3.87186i	0.979970	+	0.199147i
$379$			10.5781i			0.543361i	0.962387	+	0.271681i	$0.0875794\pi$
$379$			10.5781i			0.543361i	−0.962387	+	0.271681i	$0.912421\pi$
$380$	−6.42033	−	6.16073i	−0.329356	−	0.316039i
$381$	−12.6533	+	8.99741i	−0.648247	+	0.460951i
$382$	1.70800	+	4.00610i	0.0873891	+	0.204970i
$383$	17.4867	+	30.2878i	0.893528	+	1.54764i	0.835615	+	0.549315i	$0.185111\pi$
$383$	17.4867	+	30.2878i	0.893528	+	1.54764i	0.0579132	+	0.998322i	$0.481555\pi$
$384$	4.39047	−	19.0977i	0.224050	−	0.974578i
$385$	3.49257	−	9.18216i	0.177998	−	0.467966i
$386$	−16.7867	−	12.6079i	−0.854421	−	0.641726i
$387$	−18.9416	−	6.58459i	−0.962857	−	0.334713i
$388$	−4.99592	+	20.3123i	−0.253629	+	1.03120i
$389$	3.44020	−	5.95861i	0.174425	−	0.302113i	−0.765537	−	0.643392i	$-0.777527\pi$
$389$	3.44020	−	5.95861i	0.174425	−	0.302113i	0.939962	+	0.341278i	$0.110860\pi$
$390$	−12.7293	−	7.79850i	−0.644575	−	0.394892i
$391$		−	12.7514i		−	0.644867i
$392$	17.5422	−	9.17986i	0.886017	−	0.463653i
$393$	10.8116	−	23.6315i	0.545371	−	1.19205i
$394$	2.45733	−	20.2797i	0.123798	−	1.02168i
$395$	11.9134	+	6.87818i	0.599426	+	0.346079i
$396$	10.1189	+	19.8480i	0.508495	+	0.997402i
$397$	−15.1708	−	26.2766i	−0.761401	−	1.31879i	−0.942128	−	0.335252i	$-0.891178\pi$
$397$	−15.1708	−	26.2766i	−0.761401	−	1.31879i	0.180727	−	0.983533i	$-0.442155\pi$
$398$	15.5286	−	20.6755i	0.778380	−	1.03637i
$399$	14.3131	+	14.5191i	0.716552	+	0.726866i
$400$	3.37865	−	2.14120i	0.168933	−	0.107060i
$401$	1.04398	−	0.602741i	0.0521337	−	0.0300994i	−0.473707	−	0.880683i	$-0.657084\pi$
$401$	1.04398	−	0.602741i	0.0521337	−	0.0300994i	0.525840	+	0.850583i	$0.323751\pi$
$402$	0.275298	−	10.5602i	0.0137306	−	0.526697i
$403$	40.9435	+	23.6387i	2.03954	+	1.17753i
$404$	−13.9682	−	13.4034i	−0.694943	−	0.666843i
$405$	−8.90488	−	1.30503i	−0.442487	−	0.0648474i
$406$	2.16398	−	4.11584i	0.107396	−	0.204266i
$407$			0.201881i			0.0100069i
$408$	−9.68533	−	2.65165i	−0.479495	−	0.131276i
$409$	15.5248	+	8.96324i	0.767652	+	0.443204i	0.832036	−	0.554721i	$-0.187175\pi$
$409$	15.5248	+	8.96324i	0.767652	+	0.443204i	−0.0643847	+	0.997925i	$0.520508\pi$
$410$	2.60196	+	6.10286i	0.128502	+	0.301399i
$411$	−19.5336	+	1.85185i	−0.963523	+	0.0913450i
$412$	19.7099	−	5.71957i	0.971036	−	0.281783i
$413$	−12.1412	−	14.8999i	−0.597432	−	0.733178i
$414$	26.3313	−	1.80539i	1.29411	−	0.0887301i
$415$	6.89152	+	11.9365i	0.338291	+	0.585938i
$416$	19.5492	−	28.3967i	0.958479	−	1.39226i
$417$	−11.7930	+	8.38572i	−0.577508	+	0.410651i
$418$	−2.81031	+	23.1927i	−0.137457	+	1.13439i
$419$			9.97207i			0.487167i	0.969880	+	0.243584i	$0.0783231\pi$
$419$			9.97207i			0.487167i	−0.969880	+	0.243584i	$0.921677\pi$
$420$	−7.87473	+	4.68920i	−0.384248	+	0.228809i
$421$			7.30657i			0.356100i	0.984021	+	0.178050i	$0.0569789\pi$
$421$			7.30657i			0.356100i	−0.984021	+	0.178050i	$0.943021\pi$
$422$	−5.83602	−	0.707162i	−0.284093	−	0.0344241i
$423$	36.6771	−	7.01727i	1.78330	−	0.341191i
$424$	−4.86984	−	5.95548i	−0.236501	−	0.289224i
$425$	−1.02488	−	1.77515i	−0.0497141	−	0.0861074i
$426$	−14.3748	+	7.80703i	−0.696460	+	0.378252i
$427$	3.65174	+	22.6091i	0.176720	+	1.09413i
$428$	7.84676	+	27.0403i	0.379288	+	1.30704i
$429$	3.69922	+	39.0201i	0.178600	+	1.88391i
$430$	8.69593	−	3.70752i	0.419355	−	0.178793i
$431$	−10.2397	−	5.91190i	−0.493230	−	0.284766i	0.232684	−	0.972552i	$-0.425249\pi$
$431$	−10.2397	−	5.91190i	−0.493230	−	0.284766i	−0.725913	+	0.687786i	$0.758583\pi$
$432$	4.10429	−	20.3753i	0.197468	−	0.980309i
$433$			15.9089i			0.764532i	0.924052	+	0.382266i	$0.124856\pi$
$433$			15.9089i			0.764532i	−0.924052	+	0.382266i	$0.875144\pi$
$434$	24.5436	−	15.4955i	1.17813	−	0.743807i
$435$	−0.895532	+	1.95742i	−0.0429375	+	0.0938512i
$436$	14.3035	+	13.7251i	0.685012	+	0.657314i
$437$	23.9690	+	13.8385i	1.14659	+	0.661986i
$438$	−0.591485	+	22.6890i	−0.0282623	+	1.08412i
$439$	−16.2712	+	9.39420i	−0.776584	+	0.448361i	−0.835218	−	0.549919i	$-0.814659\pi$
$439$	−16.2712	+	9.39420i	−0.776584	+	0.448361i	0.0586346	+	0.998280i	$0.481325\pi$
$440$	−9.82252	−	3.71688i	−0.468270	−	0.177196i
$441$	18.3347	−	10.2390i	0.873082	−	0.487573i
$442$	−14.1260	−	10.6096i	−0.671907	−	0.504646i
$443$	0.548077	+	0.949297i	0.0260399	+	0.0451025i	0.878752	−	0.477279i	$-0.158377\pi$
$443$	0.548077	+	0.949297i	0.0260399	+	0.0451025i	−0.852712	+	0.522382i	$0.825044\pi$
$444$	0.116995	−	0.147599i	0.00555232	−	0.00700472i
$445$	6.22597	+	3.59457i	0.295139	+	0.170399i
$446$	32.7670	+	3.97043i	1.55156	+	0.188005i
$447$	−13.1246	−	6.00459i	−0.620773	−	0.284007i
$448$	−9.84580	−	18.7366i	−0.465170	−	0.885221i
$449$		−	14.0937i		−	0.665123i	−0.943082	−	0.332561i	$-0.892087\pi$
$449$		−	14.0937i		−	0.665123i	0.943082	−	0.332561i	$-0.107913\pi$
$450$	3.52052	−	2.36768i	0.165959	−	0.111614i
$451$	8.70950	−	15.0853i	0.410114	−	0.710338i
$452$	−0.549061	+	2.23237i	−0.0258257	+	0.105002i
$453$	3.22030	+	33.9683i	0.151303	+	1.59597i
$454$	9.68319	−	12.8926i	0.454455	−	0.605080i
$455$	−15.9180	+	2.57102i	−0.746250	+	0.120531i
$456$	15.4954	−	15.3279i	0.725637	−	0.717796i
$457$	−2.79093	−	4.83404i	−0.130554	−	0.226127i	0.793336	−	0.608784i	$-0.208342\pi$
$457$	−2.79093	−	4.83404i	−0.130554	−	0.226127i	−0.923890	+	0.382657i	$0.875009\pi$
$458$	−15.7039	+	6.69537i	−0.733794	+	0.312854i
$459$	−10.3455	−	2.53213i	−0.482888	−	0.118190i
$460$	−8.61434	+	8.97733i	−0.401646	+	0.418570i
$461$		−	28.8335i		−	1.34291i	−0.741045	−	0.671455i	$-0.765670\pi$
$461$		−	28.8335i		−	1.34291i	0.741045	−	0.671455i	$-0.234330\pi$
$462$	22.2610	+	9.13824i	1.03568	+	0.425149i
$463$	−13.5780			−0.631023			−0.315511	−	0.948922i	$-0.602176\pi$
$463$	−13.5780			−0.631023			−0.315511	+	0.948922i	$0.602176\pi$
$464$	−4.40397	−	2.30585i	−0.204449	−	0.107046i
$465$	−10.9502	+	7.78642i	−0.507804	+	0.361086i
$466$	−4.80218	−	11.2634i	−0.222457	−	0.521768i
$467$	−11.1529	+	6.43915i	−0.516097	+	0.297968i	−0.735336	−	0.677703i	$-0.762976\pi$
$467$	−11.1529	+	6.43915i	−0.516097	+	0.297968i	0.219240	+	0.975671i	$0.429642\pi$
$468$	19.9084	−	30.6720i	0.920268	−	1.41781i
$469$	−7.20775	−	8.84546i	−0.332823	−	0.408445i
$470$	−10.5716	+	14.0755i	−0.487632	+	0.649253i
$471$	2.56467	+	27.0526i	0.118174	+	1.24652i
$472$	−15.9064	+	13.0068i	−0.732153	+	0.598687i
$473$	−21.4949	−	12.4101i	−0.988339	−	0.570618i
$474$	−17.6028	+	28.7327i	−0.808523	+	1.31974i
$475$	4.44902			0.204135
$476$	−9.80137	+	4.64503i	−0.449245	+	0.212905i
$477$	−5.33510	−	6.17396i	−0.244277	−	0.282686i
$478$	9.77827	+	1.18485i	0.447248	+	0.0541938i
$479$	−1.26654	+	2.19372i	−0.0578698	+	0.100233i	−0.893509	−	0.449045i	$-0.851764\pi$
$479$	−1.26654	+	2.19372i	−0.0578698	+	0.100233i	0.835639	+	0.549279i	$0.185097\pi$
$480$	5.02738	+	8.40984i	0.229467	+	0.383855i
$481$	0.286961	−	0.165677i	0.0130843	−	0.00755421i
$482$	−12.5125	+	16.6596i	−0.569928	+	0.758825i
$483$	20.3016	−	20.0135i	0.923755	−	0.910647i
$484$	1.55350	+	5.35344i	0.0706138	+	0.243338i
$485$	−5.22943	−	9.05763i	−0.237456	−	0.411286i
$486$	3.76401	−	21.7217i	0.170739	−	0.985316i
$487$	14.2873	−	24.7464i	0.647421	−	1.12137i	−0.336315	−	0.941749i	$-0.609181\pi$
$487$	14.2873	−	24.7464i	0.647421	−	1.12137i	0.983737	−	0.179617i	$-0.0574859\pi$
$488$	24.1634	−	3.94528i	1.09383	−	0.178595i
$489$	−12.6619	+	27.6760i	−0.572592	+	1.25155i
$490$	−3.15083	+	9.38468i	−0.142340	+	0.423957i
$491$	34.4371			1.55412			0.777062	−	0.629425i	$-0.216709\pi$
$491$	34.4371			1.55412			0.777062	+	0.629425i	$0.216709\pi$
$492$	−15.1099	+	5.98174i	−0.681207	+	0.269678i
$493$	−1.27370	+	2.20611i	−0.0573646	+	0.0993584i
$494$	35.2732	−	15.0388i	1.58702	−	0.676627i
$495$	−10.5217	−	3.65761i	−0.472915	−	0.164397i
$496$	−16.6103	−	26.2098i	−0.745824	−	1.17686i
$497$	−6.28147	+	16.5144i	−0.281763	+	0.740770i
$498$	−29.6682	+	16.1130i	−1.32946	+	0.722041i
$499$	−23.2426	+	13.4191i	−1.04048	+	0.600722i	−0.919970	−	0.391990i	$-0.871787\pi$
$499$	−23.2426	+	13.4191i	−1.04048	+	0.600722i	−0.120512	+	0.992712i	$0.538454\pi$
$500$	−0.477674	+	1.94212i	−0.0213622	+	0.0868542i
$501$	−18.8776	+	13.4234i	−0.843391	+	0.599713i
$502$	−25.4203	−	3.08023i	−1.13456	−	0.137477i
$503$	27.5107			1.22664			0.613320	−	0.789834i	$-0.289834\pi$
$503$	27.5107			1.22664			0.613320	+	0.789834i	$0.289834\pi$
$504$	−10.9796	−	19.5819i	−0.489068	−	0.872245i
$505$	9.67937			0.430726
$506$	32.4296	+	3.92955i	1.44167	+	0.174690i
$507$	34.0782	−	24.2321i	1.51347	−	1.07619i
$508$	17.4091	+	4.28186i	0.772405	+	0.189977i
$509$	−16.0532	+	9.26830i	−0.711544	+	0.410810i	−0.811632	−	0.584169i	$-0.801421\pi$
$509$	−16.0532	+	9.26830i	−0.711544	+	0.410810i	0.100089	+	0.994979i	$0.468087\pi$
$510$	4.41216	−	2.39627i	0.195374	−	0.106109i
$511$	15.4861	+	19.0047i	0.685063	+	0.840720i
$512$	−20.0122	+	10.5599i	−0.884423	+	0.466686i
$513$	15.9872	−	16.6986i	0.705851	−	0.737261i
$514$	0.290007	−	0.123645i	0.0127917	−	0.00545374i
$515$	−5.13075	+	8.88672i	−0.226088	+	0.391595i
$516$	8.52335	+	21.5300i	0.375220	+	0.947807i
$517$	46.2187			2.03269
$518$	−0.00804357	−	0.203275i	−0.000353414	−	0.00893137i
$519$	3.01258	−	6.58478i	0.132237	−	0.289040i
$520$	2.77769	+	17.0124i	0.121810	+	0.746042i
$521$	−2.43582	+	4.21897i	−0.106715	+	0.184836i	−0.914438	−	0.404727i	$-0.867367\pi$
$521$	−2.43582	+	4.21897i	−0.106715	+	0.184836i	0.807722	+	0.589563i	$0.200700\pi$
$522$	−4.73589	−	2.31780i	−0.207284	−	0.101447i
$523$	4.29514	+	7.43941i	0.187813	+	0.325302i	0.944521	−	0.328451i	$-0.106527\pi$
$523$	4.29514	+	7.43941i	0.187813	+	0.325302i	−0.756707	+	0.653754i	$0.773193\pi$
$524$	−28.8187	+	8.36283i	−1.25895	+	0.365332i
$525$	1.21766	−	4.41784i	0.0531429	−	0.192810i
$526$	−2.71934	+	3.62065i	−0.118569	+	0.157868i
$527$	−13.7707	+	7.95051i	−0.599861	+	0.346330i
$528$	9.72840	−	23.8147i	0.423374	−	1.03640i
$529$	7.84991	−	13.5965i	0.341301	−	0.591150i
$530$	3.81860	+	0.462707i	0.165869	+	0.0200987i
$531$	−16.4900	+	14.2495i	−0.715603	+	0.618374i
$532$	1.90563	−	23.4648i	0.0826196	−	1.01733i
$533$	−28.5903			−1.23838
$534$	−9.19930	+	15.0158i	−0.398092	+	0.649798i
$535$	−12.1918	−	7.03895i	−0.527098	−	0.304320i
$536$	−9.44298	+	7.72160i	−0.407874	+	0.333522i
$537$	0.144062	+	1.51959i	0.00621672	+	0.0655750i
$538$	−16.3240	+	21.7345i	−0.703778	+	0.937040i
$539$	24.6701	−	8.18271i	1.06262	−	0.352454i
$540$	5.57292	+	8.77169i	0.239820	+	0.377474i
$541$	25.8855	−	14.9450i	1.11290	−	0.642536i	0.173324	−	0.984865i	$-0.444549\pi$
$541$	25.8855	−	14.9450i	1.11290	−	0.642536i	0.939580	+	0.342329i	$0.111216\pi$
$542$	0.765947	+	1.79651i	0.0329002	+	0.0771669i
$543$	12.6503	−	8.99528i	0.542875	−	0.386024i
$544$	4.98369	+	10.4696i	0.213674	+	0.448879i
$545$	−9.91171			−0.424571
$546$	−5.27944	−	39.1420i	−0.225939	−	1.67512i
$547$		−	13.9138i		−	0.594909i	−0.954736	−	0.297455i	$-0.903862\pi$
$547$		−	13.9138i		−	0.594909i	0.954736	−	0.297455i	$-0.0961377\pi$
$548$	16.3478	+	15.6867i	0.698341	+	0.670104i
$549$	25.5059	−	4.87994i	1.08857	−	0.208271i
$550$	4.83042	−	2.05946i	0.205970	−	0.0878155i
$551$	−2.76457	−	4.78838i	−0.117775	−	0.203992i
$552$	−21.4325	−	21.6666i	−0.912229	−	0.922193i
$553$	5.80332	+	35.9303i	0.246782	+	1.52791i
$554$	−6.25955	+	8.33422i	−0.265943	+	0.354087i
$555$	0.00888790	+	0.0937511i	0.000377270	+	0.00397951i
$556$	16.2256	+	3.99076i	0.688117	+	0.169246i
$557$	−10.0246	+	17.3630i	−0.424754	+	0.735695i	−0.996397	−	0.0848067i	$-0.972973\pi$
$557$	−10.0246	+	17.3630i	−0.424754	+	0.735695i	0.571643	+	0.820502i	$0.306306\pi$
$558$	−18.3673	−	27.3104i	−0.777548	−	1.15614i
$559$			40.7382i			1.72304i
$560$	10.0384	+	3.35118i	0.424200	+	0.141613i
$561$	−11.9876	−	5.48440i	−0.506118	−	0.231552i
$562$	6.81346	+	0.825599i	0.287408	+	0.0348258i
$563$	22.9242	+	13.2353i	0.966139	+	0.557800i	0.898057	−	0.439879i	$-0.144979\pi$
$563$	22.9242	+	13.2353i	0.966139	+	0.557800i	0.0680817	+	0.997680i	$0.478312\pi$
$564$	−33.7912	−	26.7847i	−1.42287	−	1.12784i
$565$	−0.574724	−	0.995451i	−0.0241788	−	0.0418789i
$566$	13.6118	+	10.2234i	0.572147	+	0.429720i
$567$	−12.2060	−	20.4454i	−0.512605	−	0.858625i
$568$	17.6661	+	6.68492i	0.741252	+	0.280493i
$569$	7.62895	−	4.40457i	0.319822	−	0.184649i	−0.331491	−	0.943458i	$-0.607552\pi$
$569$	7.62895	−	4.40457i	0.319822	−	0.184649i	0.651313	+	0.758809i	$0.274218\pi$
$570$	−0.284002	+	10.8941i	−0.0118955	+	0.456305i
$571$	34.4798	+	19.9069i	1.44294	+	0.833079i	0.998045	−	0.0625059i	$-0.0199092\pi$
$571$	34.4798	+	19.9069i	1.44294	+	0.833079i	0.444891	+	0.895585i	$0.353243\pi$
$572$	31.3356	−	32.6560i	1.31021	−	1.36542i
$573$	2.21902	−	4.85026i	0.0927010	−	0.202623i
$574$	−8.16856	+	15.5364i	−0.340949	+	0.648478i
$575$		−	6.22092i		−	0.259430i
$576$	−20.9137	+	11.7735i	−0.871406	+	0.490562i
$577$	−13.3897	−	7.73055i	−0.557421	−	0.321827i	0.194689	−	0.980865i	$-0.437630\pi$
$577$	−13.3897	−	7.73055i	−0.557421	−	0.321827i	−0.752110	+	0.659038i	$0.770964\pi$
$578$	−16.6497	+	7.09860i	−0.692534	+	0.295263i
$579$	2.42674	+	25.5977i	0.100852	+	1.06380i
$580$	2.38708	−	0.692701i	0.0991180	−	0.0287628i
$581$	−12.9644	+	34.0841i	−0.537854	+	1.41405i
$582$	22.5129	−	12.2269i	0.933188	−	0.506821i
$583$	−5.04965	−	8.74625i	−0.209135	−	0.362233i
$584$	20.2885	−	16.5901i	0.839545	−	0.686502i
$585$	3.43575	+	17.9576i	0.142051	+	0.742454i
$586$	−32.3984	−	3.92578i	−1.33837	−	0.162172i
$587$		−	15.9553i		−	0.658545i	−0.944235	−	0.329273i	$-0.893196\pi$
$587$		−	15.9553i		−	0.658545i	0.944235	−	0.329273i	$-0.106804\pi$
$588$	−22.7787	−	8.31436i	−0.939380	−	0.342878i
$589$		−	34.5132i		−	1.42209i
$590$	1.23584	−	10.1991i	0.0508786	−	0.419888i
$591$	−20.3898	+	14.4987i	−0.838725	+	0.596395i
$592$	−0.217295	+	0.00897128i	−0.00893075	+	0.000368717i
$593$	−4.15774	−	7.20142i	−0.170738	−	0.295727i	0.767940	−	0.640522i	$-0.221282\pi$
$593$	−4.15774	−	7.20142i	−0.170738	−	0.295727i	−0.938678	+	0.344795i	$0.887949\pi$
$594$	9.62788	−	25.5306i	0.395037	−	1.04753i
$595$	1.92802	−	5.06888i	0.0790411	−	0.207804i
$596$	4.64460	+	16.0055i	0.190250	+	0.655610i
$597$	−31.5276	+	2.98891i	−1.29034	+	0.122328i
$598$	−21.0282	−	49.3214i	−0.859908	−	2.01690i
$599$	−32.0559	−	18.5075i	−1.30977	−	0.756195i	−0.327711	−	0.944778i	$-0.606277\pi$
$599$	−32.0559	−	18.5075i	−1.30977	−	0.756195i	−0.982057	+	0.188583i	$0.939610\pi$
$600$	−4.72509	−	1.29363i	−0.192901	−	0.0528124i
$601$			1.41835i			0.0578558i	0.999582	+	0.0289279i	$0.00920932\pi$
$601$			1.41835i			0.0578558i	−0.999582	+	0.0289279i	$0.990791\pi$
$602$	22.1378	+	11.6393i	0.902268	+	0.474384i
$603$	−9.78939	+	8.45930i	−0.398655	+	0.344489i
$604$	27.2787	−	28.4282i	1.10995	−	1.15673i
$605$	−2.41374	−	1.39357i	−0.0981324	−	0.0566568i
$606$	−0.617879	+	23.7015i	−0.0250996	+	0.962806i
$607$	0.559732	−	0.323161i	0.0227188	−	0.0131167i	−0.488598	−	0.872509i	$-0.662491\pi$
$607$	0.559732	−	0.323161i	0.0227188	−	0.0131167i	0.511316	+	0.859393i	$0.329158\pi$
$608$	−25.0883	−	1.99422i	−1.01747	−	0.0808763i
$609$	−5.51145	+	1.43466i	−0.223335	+	0.0581354i
$610$	−7.35169	+	9.78835i	−0.297661	+	0.396319i
$611$	−37.9300	−	65.6967i	−1.53448	−	2.65781i
$612$	5.58600	+	10.9568i	0.225801	+	0.442903i
$613$	−27.9219	−	16.1207i	−1.12776	−	0.651110i	−0.184386	−	0.982854i	$-0.559030\pi$
$613$	−27.9219	−	16.1207i	−1.12776	−	0.651110i	−0.943369	+	0.331744i	$0.892363\pi$
$614$	1.21763	−	10.0488i	0.0491397	−	0.405537i
$615$	3.38045	−	7.38886i	0.136313	−	0.297948i
$616$	−8.79286	−	26.3584i	−0.354274	−	1.06201i
$617$		−	29.0671i		−	1.17020i	−0.810961	−	0.585100i	$-0.801055\pi$
$617$		−	29.0671i		−	1.17020i	0.810961	−	0.585100i	$-0.198945\pi$
$618$	−21.4330	−	13.1307i	−0.862162	−	0.528195i
$619$	−8.54194	+	14.7951i	−0.343330	+	0.594664i	−0.985049	−	0.172275i	$-0.944888\pi$
$619$	−8.54194	+	14.7951i	−0.343330	+	0.594664i	0.641719	+	0.766940i	$0.278221\pi$
$620$	15.0660	+	3.70555i	0.605064	+	0.148818i
$621$	−23.3491	−	22.3543i	−0.936967	−	0.897048i
$622$	26.3462	+	19.7877i	1.05639	+	0.793415i
$623$	3.03284	+	18.7773i	0.121508	+	0.752297i
$624$	−41.8348	+	5.71564i	−1.67473	+	0.228809i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−1.62571	−	3.81307i	−0.0649764	−	0.152401i
$627$	23.3187	−	16.5813i	0.931258	−	0.662193i
$628$	21.7249	−	22.6404i	0.866919	−	0.903449i
$629$			0.111446i			0.00444363i
$630$	10.7401	+	3.26363i	0.427894	+	0.130026i
$631$	−19.4033			−0.772431			−0.386216	−	0.922409i	$-0.626218\pi$
$631$	−19.4033			−0.772431			−0.386216	+	0.922409i	$0.626218\pi$
$632$	38.4004	−	6.26982i	1.52749	−	0.249400i
$633$	4.17238	+	5.86772i	0.165837	+	0.233221i
$634$	20.1249	−	8.58027i	0.799261	−	0.340766i
$635$	−7.76303	+	4.48199i	−0.308067	+	0.177862i
$636$	−1.37677	+	9.32090i	−0.0545924	+	0.369598i
$637$	−31.8771	−	28.3516i	−1.26301	−	1.12333i
$638$	−5.21811	−	3.91914i	−0.206587	−	0.155160i
$639$	18.9236	+	6.57831i	0.748605	+	0.260234i
$640$	3.56417	−	10.7376i	0.140886	−	0.424442i
$641$	2.54419	+	1.46889i	0.100489	+	0.0580176i	0.549402	−	0.835558i	$-0.314855\pi$
$641$	2.54419	+	1.46889i	0.100489	+	0.0580176i	−0.448913	+	0.893575i	$0.648189\pi$
$642$	18.0142	−	29.4042i	0.710965	−	1.16049i
$643$	−45.2268			−1.78357			−0.891786	−	0.452458i	$-0.850547\pi$
$643$	−45.2268			−1.78357			−0.891786	+	0.452458i	$0.850547\pi$
$644$	−32.8100	−	2.66458i	−1.29289	−	0.104999i
$645$	−10.5283	−	4.81678i	−0.414553	−	0.189660i
$646$	−1.55139	+	12.8032i	−0.0610386	+	0.503735i
$647$	−6.85135	+	11.8669i	−0.269354	+	0.466535i	−0.968695	−	0.248253i	$-0.920144\pi$
$647$	−6.85135	+	11.8669i	−0.269354	+	0.466535i	0.699341	+	0.714788i	$0.253477\pi$
$648$	−21.8346	+	13.0862i	−0.857745	+	0.514075i
$649$	−23.3603	+	13.4871i	−0.916970	+	0.529413i
$650$	−6.89153	−	5.17599i	−0.270308	−	0.203019i
$651$	−34.2713	−	9.44595i	−1.34320	−	0.370216i
$652$	33.7509	−	9.79410i	1.32179	−	0.383566i
$653$	−1.21773	−	2.10917i	−0.0476534	−	0.0825380i	0.841215	−	0.540701i	$-0.181841\pi$
$653$	−1.21773	−	2.10917i	−0.0476534	−	0.0825380i	−0.888868	+	0.458163i	$0.848508\pi$
$654$	0.632711	−	24.2704i	0.0247410	−	0.949047i
$655$	7.50189	−	12.9937i	0.293123	−	0.507704i
$656$	16.6241	+	8.70409i	0.649061	+	0.339838i
$657$	21.0328	−	18.1751i	0.820568	−	0.709077i
$658$	−46.5376	+	1.84149i	−1.81423	+	0.0717889i
$659$	35.6881			1.39021			0.695106	−	0.718907i	$-0.255357\pi$
$659$	35.6881			1.39021			0.695106	+	0.718907i	$0.255357\pi$
$660$	4.73455	+	11.9595i	0.184292	+	0.465523i
$661$	−0.137767	+	0.238619i	−0.00535850	+	0.00928120i	−0.868692	−	0.495352i	$-0.835039\pi$
$661$	−0.137767	+	0.238619i	−0.00535850	+	0.00928120i	0.863334	+	0.504633i	$0.168372\pi$
$662$	3.75280	+	8.80213i	0.145857	+	0.342105i
$663$	2.04210	+	21.5405i	0.0793087	+	0.836562i
$664$	36.4612	+	13.7971i	1.41497	+	0.535430i
$665$	7.43564	+	9.12513i	0.288342	+	0.353857i
$666$	−0.230132	+	0.0157789i	−0.00891743	+	0.000611418i
$667$	−6.69543	+	3.86561i	−0.259248	+	0.149677i
$668$	25.9730	+	6.38818i	1.00492	+	0.247166i
$669$	−23.4263	−	32.9449i	−0.905711	−	1.27372i
$670$	0.733665	−	6.05475i	0.0283439	−	0.233915i
$671$	32.1413			1.24080
$672$	−8.84669	+	24.3667i	−0.341268	+	0.939966i
$673$	−29.9243			−1.15350			−0.576748	−	0.816922i	$-0.695678\pi$
$673$	−29.9243			−1.15350			−0.576748	+	0.816922i	$0.695678\pi$
$674$	−5.18996	+	42.8314i	−0.199910	+	1.64980i
$675$	−5.04717	−	1.23532i	−0.194266	−	0.0475477i
$676$	−46.8868	−	11.5320i	−1.80334	−	0.443540i
$677$	34.4393	−	19.8835i	1.32361	−	0.764186i	0.339306	−	0.940676i	$-0.389808\pi$
$677$	34.4393	−	19.8835i	1.32361	−	0.764186i	0.984302	+	0.176491i	$0.0564745\pi$
$678$	2.47421	−	1.34376i	0.0950213	−	0.0516067i
$679$	9.83765	−	25.8638i	0.377534	−	0.992560i
$680$	−5.42238	−	2.05185i	−0.207939	−	0.0786850i
$681$	−19.6596	+	1.86380i	−0.753359	+	0.0714208i
$682$	−15.9762	−	37.4719i	−0.611760	−	1.43487i
$683$	25.5875	−	44.3189i	0.979079	−	1.69582i	0.313322	−	0.949647i	$-0.398558\pi$
$683$	25.5875	−	44.3189i	0.979079	−	1.69582i	0.665758	−	0.746168i	$-0.268108\pi$
$684$	−26.6579	−	1.39085i	−1.01929	−	0.0531804i
$685$	−11.3283			−0.432833
$686$	−24.5143	+	9.22212i	−0.935962	+	0.352102i
$687$	19.0130	+	8.69857i	0.725392	+	0.331871i
$688$	12.4024	−	23.6875i	0.472837	−	0.903079i
$689$	−8.28814	+	14.3555i	−0.315753	+	0.546900i
$690$	15.2329	+	0.397110i	0.579907	+	0.0151177i
$691$	14.3455	+	24.8471i	0.545727	+	0.945227i	0.998561	+	0.0536321i	$0.0170798\pi$
$691$	14.3455	+	24.8471i	0.545727	+	0.945227i	−0.452834	+	0.891595i	$0.649587\pi$
$692$	−8.03015	+	2.33025i	−0.305260	+	0.0885829i
$693$	−10.0830	−	27.6934i	−0.383021	−	1.05198i
$694$	−33.1545	−	24.9012i	−1.25853	−	0.945237i
$695$	−7.23526	+	4.17728i	−0.274449	+	0.158453i
$696$	1.54381	+	5.88935i	0.0585180	+	0.223235i
$697$	4.80795	−	8.32762i	0.182114	−	0.315431i
$698$	−0.649955	+	5.36391i	−0.0246012	+	0.203027i
$699$	−6.23895	+	13.6369i	−0.235979	+	0.515794i
$700$	−4.78170	+	2.26613i	−0.180731	+	0.0856516i
$701$	5.54707			0.209510			0.104755	−	0.994498i	$-0.466594\pi$
$701$	5.54707			0.209510			0.104755	+	0.994498i	$0.466594\pi$
$702$	−44.1913	+	7.26665i	−1.66789	+	0.274262i
$703$	−0.209486	−	0.120947i	−0.00790090	−	0.00456159i
$704$	−28.1622	+	9.44823i	−1.06140	+	0.356094i
$705$	21.4634	−	2.03479i	0.808357	−	0.0766348i
$706$	−5.64432	−	4.23925i	−0.212427	−	0.159546i
$707$	16.1771	+	19.8528i	0.608402	+	0.746641i
$708$	24.8951	+	3.67720i	0.935615	+	0.138198i
$709$	−21.2936	+	12.2939i	−0.799699	+	0.461706i	−0.843366	−	0.537340i	$-0.819429\pi$
$709$	−21.2936	+	12.2939i	−0.799699	+	0.461706i	0.0436669	+	0.999046i	$0.486096\pi$
$710$	−8.68764	+	3.70399i	−0.326041	+	0.139008i
$711$	40.5339	−	7.75518i	1.52014	−	0.290842i
$712$	20.0682	−	3.27663i	0.752088	−	0.122797i
$713$	−48.2587			−1.80730
$714$	12.2889	+	5.04463i	0.459899	+	0.188791i
$715$			22.6293i			0.846286i
$716$	1.22032	−	1.27175i	0.0456057	−	0.0475274i
$717$	−6.99083	−	9.83138i	−0.261077	−	0.367160i
$718$	10.4797	+	24.5799i	0.391098	+	0.917315i
$719$	−13.2217	−	22.9007i	−0.493087	−	0.854051i	0.506882	−	0.862016i	$-0.330798\pi$
$719$	−13.2217	−	22.9007i	−0.493087	−	0.854051i	−0.999968	+	0.00796455i	$0.997465\pi$
$720$	3.46929	−	11.4876i	0.129293	−	0.428116i
$721$	−26.8020	+	4.32896i	−0.998159	+	0.161219i
$722$	−0.897637	−	0.674184i	−0.0334066	−	0.0250905i
$723$	25.4039	−	2.40837i	0.944781	−	0.0895682i
$724$	−17.4050	−	4.28084i	−0.646851	−	0.159096i
$725$	−0.621388	+	1.07628i	−0.0230778	+	0.0399719i
$726$	3.56646	−	5.82146i	0.132364	−	0.216055i
$727$			7.18001i			0.266292i	0.991096	+	0.133146i	$0.0425079\pi$
$727$			7.18001i			0.266292i	−0.991096	+	0.133146i	$0.957492\pi$
$728$	−30.2507	+	34.1299i	−1.12117	+	1.26494i
$729$	−22.7731	+	14.5046i	−0.843450	+	0.537208i
$730$	−1.57630	+	13.0088i	−0.0583415	+	0.481477i
$731$	−11.8660	−	6.85082i	−0.438879	−	0.253387i
$732$	−23.4990	−	18.6266i	−0.868549	−	0.688460i
$733$	17.3916	+	30.1232i	0.642374	+	1.11263i	0.984901	+	0.173117i	$0.0553839\pi$
$733$	17.3916	+	30.1232i	0.642374	+	1.11263i	−0.342527	+	0.939508i	$0.611283\pi$
$734$	−0.564693	+	0.751855i	−0.0208432	+	0.0277515i
$735$	11.0962	−	4.88606i	0.409291	−	0.180225i
$736$	−2.78845	+	35.0802i	−0.102784	+	1.29307i
$737$	−13.8680	+	8.00669i	−0.510834	+	0.294930i
$738$	17.8770	+	8.74922i	0.658061	+	0.322063i
$739$	34.3522	+	19.8332i	1.26367	+	0.729577i	0.973782	−	0.227484i	$-0.0730501\pi$
$739$	34.3522	+	19.8332i	1.26367	+	0.729577i	0.289884	+	0.957062i	$0.406383\pi$
$740$	0.0752881	−	0.0784606i	0.00276765	−	0.00288427i
$741$	−42.7060	−	19.5383i	−1.56885	−	0.717756i
$742$	5.43298	+	8.60542i	0.199451	+	0.315915i
$743$		−	41.7771i		−	1.53265i	−0.642451	−	0.766327i	$-0.722082\pi$
$743$		−	41.7771i		−	1.53265i	0.642451	−	0.766327i	$-0.277918\pi$
$744$	−10.0353	+	36.6548i	−0.367914	+	1.34383i
$745$	−7.21649	−	4.16644i	−0.264392	−	0.152647i
$746$	7.34088	+	17.2179i	0.268769	+	0.630392i
$747$	39.0565	+	13.5770i	1.42900	+	0.496757i
$748$	4.24223	+	14.6189i	0.155111	+	0.534520i
$749$	−5.93896	−	36.7701i	−0.217005	−	1.34355i
$750$	2.15252	−	1.16905i	0.0785988	−	0.0426875i
$751$	−13.7157	−	23.7564i	−0.500494	−	0.866882i	−1.00000		0.000570880i	$-0.999818\pi$
$751$	−13.7157	−	23.7564i	−0.500494	−	0.866882i	0.499506	−	0.866311i	$-0.333515\pi$
$752$	2.05388	+	49.7474i	0.0748974	+	1.81410i
$753$	18.1739	+	25.5584i	0.662293	+	0.931399i
$754$	−1.28848	+	10.6335i	−0.0469237	+	0.387249i
$755$			19.6995i			0.716940i
$756$	−8.67711	+	26.0904i	−0.315583	+	0.948898i
$757$		−	21.1452i		−	0.768534i	−0.923222	−	0.384267i	$-0.874454\pi$
$757$		−	21.1452i		−	0.768534i	0.923222	−	0.384267i	$-0.125546\pi$
$758$	−14.8511	−	1.79953i	−0.539416	−	0.0653620i
$759$	−23.1851	−	32.6057i	−0.841565	−	1.18351i
$760$	9.74154	−	7.96573i	0.353363	−	0.288948i
$761$	−23.2981	−	40.3535i	−0.844556	−	1.46281i	−0.886006	−	0.463673i	$-0.846531\pi$
$761$	−23.2981	−	40.3535i	−0.844556	−	1.46281i	0.0414503	−	0.999141i	$-0.486802\pi$
$762$	−10.4793	−	19.2951i	−0.379625	−	0.698988i
$763$	−16.5654	−	20.3293i	−0.599708	−	0.735971i
$764$	−5.91490	+	1.71643i	−0.213994	+	0.0620983i
$765$	−5.80835	−	2.01913i	−0.210001	−	0.0730018i
$766$	−45.4973	+	19.3978i	−1.64388	+	0.700872i
$767$	38.3419	+	22.1367i	1.38445	+	0.799310i
$768$	26.0653	+	9.41286i	0.940549	+	0.339657i
$769$		−	32.8936i		−	1.18618i	−0.805138	−	0.593088i	$-0.797909\pi$
$769$		−	32.8936i		−	1.18618i	0.805138	−	0.593088i	$-0.202091\pi$
$770$	12.2971	+	6.46542i	0.443156	+	0.232998i
$771$	−0.351117	−	0.160638i	−0.0126452	−	0.00578525i
$772$	20.5566	−	21.4228i	0.739847	−	0.771022i
$773$	10.0725	+	5.81534i	0.362281	+	0.209163i	0.670081	−	0.742288i	$-0.266259\pi$
$773$	10.0725	+	5.81534i	0.362281	+	0.209163i	−0.307800	+	0.951451i	$0.599593\pi$
$774$	12.4667	−	25.4728i	0.448107	−	0.915602i
$775$	−6.71818	+	3.87874i	−0.241324	+	0.139329i
$776$	−27.6675	−	10.4695i	−0.993205	−	0.375833i
$777$	−0.177433	+	0.174915i	−0.00636538	+	0.00627505i
$778$	7.78031	+	5.84353i	0.278938	+	0.209501i
$779$	10.4357	+	18.0751i	0.373897	+	0.647608i
$780$	13.1142	−	16.5446i	0.469562	−	0.592392i
$781$	21.4744	+	12.3983i	0.768416	+	0.443645i
$782$	17.9023	+	2.16925i	0.640185	+	0.0775724i
$783$	1.80670	+	6.19977i	0.0645663	+	0.221562i
$784$	9.90375	+	26.1900i	0.353705	+	0.935357i
$785$			15.6888i			0.559959i
$786$	31.3381	+	19.1990i	1.11779	+	0.684806i
$787$	−9.26180	+	16.0419i	−0.330147	+	0.571832i	−0.982541	−	0.186049i	$-0.940432\pi$
$787$	−9.26180	+	16.0419i	−0.330147	+	0.571832i	0.652393	+	0.757881i	$0.273765\pi$
$788$	28.0535	+	6.89990i	0.999365	+	0.245799i
$789$	5.52104	−	0.523412i	0.196554	−	0.0186340i
$790$	−11.6833	+	15.5556i	−0.415672	+	0.553443i
$791$	1.08118	−	2.84248i	0.0384422	−	0.101067i
$792$	−29.5870	+	10.8299i	−1.05133	+	0.384823i
$793$	−26.3773	−	45.6868i	−0.936684	−	1.62238i
$794$	39.4717	−	16.8288i	1.40080	−	0.597233i
$795$	−2.73005	−	3.83934i	−0.0968249	−	0.136167i
$796$	26.3855	+	25.3186i	0.935209	+	0.897395i
$797$			0.954691i			0.0338169i	0.999857	+	0.0169084i	$0.00538238\pi$
$797$			0.954691i			0.0338169i	−0.999857	+	0.0169084i	$0.994618\pi$
$798$	−22.8190	+	17.6248i	−0.807783	+	0.623912i
$799$	25.5143			0.902632
$800$	2.43135	+	5.10769i	0.0859611	+	0.180584i
$801$	21.1832	−	4.05289i	0.748471	−	0.143202i
$802$	0.668614	+	1.56822i	0.0236096	+	0.0553759i
$803$	29.7958	−	17.2026i	1.05147	−	0.607067i
$804$	14.7792	+	2.18300i	0.521221	+	0.0769884i
$805$	12.7594	−	10.3970i	0.449708	−	0.366446i
$806$	−40.1527	+	53.4610i	−1.41432	+	1.88308i
$807$	33.1424	−	3.14200i	1.16667	−	0.110604i
$808$	21.1939	−	17.3304i	0.745597	−	0.609681i
$809$	46.4968	+	26.8449i	1.63474	+	0.943817i	0.982604	+	0.185715i	$0.0594602\pi$
$809$	46.4968	+	26.8449i	1.63474	+	0.943817i	0.652136	+	0.758102i	$0.273873\pi$
$810$	3.34707	−	12.2799i	0.117604	−	0.431473i
$811$	8.29444			0.291257			0.145629	−	0.989339i	$-0.453480\pi$
$811$	8.29444			0.291257			0.145629	+	0.989339i	$0.453480\pi$
$812$	5.41027	+	3.73828i	0.189863	+	0.131188i
$813$	0.995111	−	2.17508i	0.0349001	−	0.0762833i
$814$	−0.283430	−	0.0343437i	−0.00993422	−	0.00120375i
$815$	−8.78580	+	15.2175i	−0.307753	+	0.533044i
$816$	5.37042	−	13.1466i	0.188002	−	0.460222i
$817$	25.7551	−	14.8697i	0.901058	−	0.520226i
$818$	−15.2249	+	20.2711i	−0.532328	+	0.708763i
$819$	−31.0896	+	37.0593i	−1.08636	+	1.29496i
$820$	−9.01072	+	2.61480i	−0.314668	+	0.0913128i
$821$	−2.08024	−	3.60308i	−0.0726008	−	0.125748i	0.827440	−	0.561555i	$-0.189797\pi$
$821$	−2.08024	−	3.60308i	−0.0726008	−	0.125748i	−0.900040	+	0.435806i	$0.856463\pi$
$822$	0.723139	−	27.7392i	0.0252224	−	0.967515i
$823$	13.8704	−	24.0243i	0.483492	−	0.837433i	−0.516328	−	0.856391i	$-0.672701\pi$
$823$	13.8704	−	24.0243i	0.483492	−	0.837433i	0.999820	+	0.0189578i	$0.00603480\pi$
$824$	4.67694	+	28.6446i	0.162929	+	0.997882i
$825$	−5.84829	−	2.67562i	−0.203611	−	0.0931533i
$826$	22.9841	−	14.5109i	0.799720	−	0.504898i
$827$	−1.12502			−0.0391208			−0.0195604	−	0.999809i	$-0.506227\pi$
$827$	−1.12502			−0.0391208			−0.0195604	+	0.999809i	$0.506227\pi$
$828$	−1.94477	+	37.2748i	−0.0675856	+	1.29539i
$829$	0.00110719	−	0.00191771i	3.84543e−5	−	6.66048e-5i	−0.866006	−	0.500033i	$-0.833321\pi$
$829$	0.00110719	−	0.00191771i	3.84543e−5	−	6.66048e-5i	0.866045	+	0.499967i	$0.166654\pi$
$830$	−17.9305	+	7.64469i	−0.622377	+	0.265351i
$831$	12.7087	−	1.20482i	0.440859	−	0.0417948i
$832$	36.5417	+	32.2768i	1.26686	+	1.11900i
$833$	13.6188	−	4.51715i	0.471862	−	0.156510i
$834$	−9.76687	−	17.9833i	−0.338199	−	0.622712i
$835$	−11.5818	+	6.68676i	−0.400805	+	0.231405i
$836$	−32.0832	−	7.89102i	−1.10962	−	0.272917i
$837$	−9.58301	+	39.1534i	−0.331237	+	1.35334i
$838$	−14.0002	−	1.69643i	−0.483630	−	0.0586023i
$839$	−31.8724			−1.10036			−0.550178	−	0.835047i	$-0.685440\pi$
$839$	−31.8724			−1.10036			−0.550178	+	0.835047i	$0.685440\pi$
$840$	−5.24373	−	11.8534i	−0.180926	−	0.408981i
$841$	−27.4555			−0.946742
$842$	−10.2580	−	1.24298i	−0.353515	−	0.0428360i
$843$	−4.87118	−	6.85046i	−0.167772	−	0.235942i
$844$	1.98563	−	8.07315i	0.0683482	−	0.277889i
$845$	20.9076	−	12.0710i	0.719245	−	0.415256i
$846$	3.61241	+	52.6863i	0.124197	+	1.81139i
$847$	−1.17580	−	7.27975i	−0.0404009	−	0.250135i
$848$	9.18961	−	5.82385i	0.315573	−	0.199992i
$849$	−1.96776	−	20.7563i	−0.0675335	−	0.712355i
$850$	2.66656	−	1.13689i	0.0914623	−	0.0389951i
$851$	−0.169115	+	0.292917i	−0.00579720	+	0.0100411i
$852$	−8.51522	−	21.5095i	−0.291727	−	0.736903i
$853$	19.0335			0.651696			0.325848	−	0.945422i	$-0.394350\pi$
$853$	19.0335			0.651696			0.325848	+	0.945422i	$0.394350\pi$
$854$	−32.3632	+	1.28061i	−1.10744	+	0.0438216i
$855$	10.0989	−	8.72676i	0.345375	−	0.298449i
$856$	−39.2979	+	6.41636i	−1.34318	+	0.219307i
$857$	17.5296	−	30.3621i	0.598799	−	1.03715i	−0.394199	−	0.919025i	$-0.628978\pi$
$857$	17.5296	−	30.3621i	0.598799	−	1.03715i	0.992999	−	0.118126i	$-0.0376886\pi$
$858$	−55.4113	−	1.44453i	−1.89171	−	0.0493155i
$859$	−14.4471	−	25.0231i	−0.492928	−	0.853776i	0.507039	−	0.861923i	$-0.330740\pi$
$859$	−14.4471	−	25.0231i	−0.492928	−	0.853776i	−0.999967	+	0.00814729i	$0.997407\pi$
$860$	3.72582	+	12.8393i	0.127049	+	0.437817i
$861$	20.8046	−	5.41554i	0.709018	−	0.184561i
$862$	10.0419	−	13.3703i	0.342030	−	0.455393i
$863$	−13.8732	+	8.00968i	−0.472248	+	0.272653i	−0.717180	−	0.696888i	$-0.754568\pi$
$863$	−13.8732	+	8.00968i	−0.472248	+	0.272653i	0.244932	+	0.969540i	$0.421234\pi$
$864$	27.9076	+	9.22842i	0.949437	+	0.313957i
$865$	2.09035	−	3.62060i	0.0710742	−	0.123104i
$866$	−22.3352	−	2.70640i	−0.758980	−	0.0919671i
$867$	20.1581	+	9.22244i	0.684604	+	0.313210i
$868$	17.5795	+	37.0940i	0.596686	+	1.25905i
$869$	51.0788			1.73273
$870$	−2.59577	−	1.59027i	−0.0880047	−	0.0539152i
$871$	22.7620	+	13.1416i	0.771260	+	0.445287i
$872$	−21.7026	+	17.7464i	−0.734942	+	0.600968i
$873$	−29.6369	−	10.3025i	−1.00306	−	0.348688i
$874$	−23.5061	+	31.2970i	−0.795105	+	1.05864i
$875$	0.940605	−	2.47291i	0.0317983	−	0.0835995i
$876$	−31.7535	−	4.69023i	−1.07285	−	0.158468i
$877$	−22.6522	+	13.0782i	−0.764910	+	0.441621i	−0.831056	−	0.556189i	$-0.812263\pi$
$877$	−22.6522	+	13.0782i	−0.764910	+	0.441621i	0.0661458	+	0.997810i	$0.478930\pi$
$878$	−10.4209	−	24.4420i	−0.351688	−	0.824879i
$879$	23.1628	+	32.5744i	0.781261	+	1.09871i
$880$	6.88929	−	13.1580i	0.232238	−	0.443555i
$881$	25.2590			0.850998			0.425499	−	0.904959i	$-0.360099\pi$
$881$	25.2590			0.850998			0.425499	+	0.904959i	$0.360099\pi$
$882$	11.2560	+	27.4828i	0.379008	+	0.925393i
$883$		−	53.2980i		−	1.79362i	−0.442416	−	0.896810i	$-0.645878\pi$
$883$		−	53.2980i		−	1.79362i	0.442416	−	0.896810i	$-0.354122\pi$
$884$	17.2983	−	18.0273i	0.581806	−	0.606323i
$885$	−10.2544	+	7.29166i	−0.344699	+	0.245107i
$886$	−1.42600	+	0.607977i	−0.0479074	+	0.0204254i
$887$	−29.4551	−	51.0177i	−0.989005	−	1.71301i	−0.622572	−	0.782562i	$-0.713912\pi$
$887$	−29.4551	−	51.0177i	−0.989005	−	1.71301i	−0.366433	−	0.930445i	$-0.619421\pi$
$888$	0.187317	+	0.189363i	0.00628595	+	0.00635462i
$889$	−22.1671	−	8.43157i	−0.743460	−	0.282786i
$890$	−6.10572	+	8.12942i	−0.204664	+	0.272499i
$891$	−31.0578	+	12.3359i	−1.04047	+	0.413267i
$892$	−11.1485	+	45.3275i	−0.373280	+	1.51768i
$893$	−27.6895	+	47.9596i	−0.926593	+	1.60491i
$894$	10.6628	−	17.4047i	0.356619	−	0.582102i
$895$			0.881268i			0.0294575i
$896$	27.9801	−	10.6355i	0.934749	−	0.355307i
$897$	−27.3197	+	59.7144i	−0.912178	+	1.99381i
$898$	19.7868	+	2.39760i	0.660293	+	0.0800089i
$899$	8.34919	+	4.82041i	0.278461	+	0.160770i
$900$	2.72519	+	5.34540i	0.0908397	+	0.178180i
$901$	−2.78759	−	4.82824i	−0.0928679	−	0.160852i
$902$	19.6973	+	14.7939i	0.655847	+	0.492584i
$903$	−7.71658	−	29.6443i	−0.256792	−	0.986502i
$904$	−3.04071	−	1.15062i	−0.101133	−	0.0382690i
$905$	7.76119	−	4.48093i	0.257991	−	0.148951i
$906$	−48.2374	−	1.25751i	−1.60258	−	0.0417781i
$907$	12.6965	+	7.33031i	0.421580	+	0.243399i	0.695753	−	0.718281i	$-0.255071\pi$
$907$	12.6965	+	7.33031i	0.421580	+	0.243399i	−0.274173	+	0.961680i	$0.588404\pi$
$908$	16.4532	+	15.7879i	0.546019	+	0.523941i
$909$	21.9714	−	18.9861i	0.728744	−	0.629729i
$910$	−0.901619	−	22.7854i	−0.0298884	−	0.755330i
$911$			40.0568i			1.32714i	0.748114	+	0.663571i	$0.230960\pi$
$911$			40.0568i			1.32714i	−0.748114	+	0.663571i	$0.769040\pi$
$912$	18.8835	+	24.3622i	0.625295	+	0.806713i
$913$	44.3213	+	25.5889i	1.46682	+	0.846870i
$914$	7.26151	−	3.09595i	0.240189	−	0.102405i
$915$	14.9260	−	1.41504i	0.493440	−	0.0467796i
$916$	−6.72841	−	23.1864i	−0.222313	−	0.766100i
$917$	39.1884	−	6.32956i	1.29411	−	0.209021i
$918$	5.31493	−	14.0938i	0.175419	−	0.465164i
$919$	−3.35888	−	5.81776i	−0.110799	−	0.191910i	0.805293	−	0.592876i	$-0.202008\pi$
$919$	−3.35888	−	5.81776i	−0.110799	−	0.191910i	−0.916093	+	0.400966i	$0.868674\pi$
$920$	−11.1382	−	13.6213i	−0.367216	−	0.449080i
$921$	−10.1034	+	7.18425i	−0.332918	+	0.236729i
$922$	40.4806	+	4.90511i	1.33316	+	0.161541i
$923$		−	40.6993i		−	1.33963i
$924$	−16.6166	+	29.6986i	−0.546646	+	0.977013i
$925$			0.0543699i			0.00178767i
$926$	2.30987	−	19.0627i	0.0759070	−	0.626441i
$927$	5.78494	+	30.2361i	0.190002	+	0.993082i
$928$	3.98648	−	5.79066i	0.130863	−	0.190088i
$929$	22.3117	+	38.6450i	0.732022	+	1.26790i	0.956018	+	0.293310i	$0.0947567\pi$
$929$	22.3117	+	38.6450i	0.732022	+	1.26790i	−0.223995	+	0.974590i	$0.571910\pi$
$930$	−9.06886	−	16.6981i	−0.297380	−	0.547553i
$931$	−6.28886	+	30.5016i	−0.206109	+	0.999649i
$932$	16.6302	−	4.82588i	0.544739	−	0.158077i
$933$	−3.80869	−	40.1747i	−0.124691	−	1.31526i
$934$	−7.14289	−	16.7535i	−0.233723	−	0.548192i
$935$	−6.59131	−	3.80550i	−0.215559	−	0.124453i
$936$	39.6749	+	33.1682i	1.29682	+	1.08414i
$937$			6.28708i			0.205390i	0.994713	+	0.102695i	$0.0327466\pi$
$937$			6.28708i			0.205390i	−0.994713	+	0.102695i	$0.967253\pi$
$938$	13.6447	−	8.61450i	0.445515	−	0.281273i
$939$	−2.11210	+	4.61656i	−0.0689259	+	0.150656i
$940$	−17.9628	−	17.2364i	−0.585880	−	0.562191i
$941$	−40.2732	−	23.2517i	−1.31287	−	0.757985i	−0.330298	−	0.943877i	$-0.607149\pi$
$941$	−40.2732	−	23.2517i	−1.31287	−	0.757985i	−0.982570	+	0.185892i	$0.940483\pi$
$942$	−38.4166	−	1.00149i	−1.25168	−	0.0326304i
$943$	25.2738	−	14.5919i	0.823029	−	0.475176i
$944$	−15.5549	−	24.5444i	−0.506268	−	0.798854i
$945$	−5.90162	−	12.4166i	−0.191980	−	0.403911i
$946$	21.0798	−	28.0665i	0.685363	−	0.912521i
$947$	1.78889	+	3.09844i	0.0581310	+	0.100686i	0.893626	−	0.448812i	$-0.148153\pi$
$947$	1.78889	+	3.09844i	0.0581310	+	0.100686i	−0.835495	+	0.549497i	$0.814819\pi$
$948$	−37.3445	−	29.6013i	−1.21289	−	0.961406i
$949$	−48.9048	−	28.2352i	−1.58752	−	0.916552i
$950$	−0.756861	+	6.24618i	−0.0245558	+	0.202653i
$951$	−24.3656	−	11.1474i	−0.790109	−	0.361480i
$952$	−4.85397	−	14.5508i	−0.157318	−	0.471593i
$953$			27.3490i			0.885921i	0.896541	+	0.442960i	$0.146072\pi$
$953$			27.3490i			0.885921i	−0.896541	+	0.442960i	$0.853928\pi$
$954$	9.57549	−	6.43988i	0.310018	−	0.208499i
$955$	1.53973	−	2.66689i	0.0498244	−	0.0862984i
$956$	−3.32693	+	13.5266i	−0.107601	+	0.437481i
$957$	0.754346	+	7.95697i	0.0243845	+	0.257212i
$958$	−2.86439	−	2.15135i	−0.0925443	−	0.0695068i
$959$	−18.9330	−	23.2348i	−0.611377	−	0.750292i
$960$	−12.6622	+	5.62749i	−0.408671	+	0.181627i
$961$	14.5893	+	25.2694i	0.470622	+	0.815141i
$962$	0.183784	+	0.431062i	0.00592543	+	0.0138980i
$963$	−41.4813	+	7.93644i	−1.33672	+	0.255748i
$964$	−21.2606	−	20.4009i	−0.684757	−	0.657070i
$965$			14.8451i			0.477880i
$966$	24.6442	+	31.9070i	0.792914	+	1.02659i
$967$	−23.5270			−0.756577			−0.378288	−	0.925688i	$-0.623487\pi$
$967$	−23.5270			−0.756577			−0.378288	+	0.925688i	$0.623487\pi$
$968$	−7.78021	+	1.27031i	−0.250065	+	0.0408294i
$969$	12.8727	−	9.15347i	0.413532	−	0.294052i
$970$	13.6060	−	5.80095i	0.436863	−	0.186257i
$971$	−39.1004	+	22.5746i	−1.25479	+	0.724454i	−0.972057	−	0.234744i	$-0.924575\pi$
$971$	−39.1004	+	22.5746i	−1.25479	+	0.724454i	−0.282734	+	0.959198i	$0.591241\pi$
$972$	29.8557	+	8.97972i	0.957623	+	0.288025i
$973$	−20.6600	−	7.85835i	−0.662331	−	0.251927i
$974$	32.3120	+	24.2685i	1.03534	+	0.777612i
$975$	0.996262	+	10.5087i	0.0319059	+	0.336549i
$976$	1.42831	+	34.5953i	0.0457191	+	1.10737i
$977$	−1.31173	−	0.757327i	−0.0419659	−	0.0242290i	0.478870	−	0.877886i	$-0.341046\pi$
$977$	−1.31173	−	0.757327i	−0.0419659	−	0.0242290i	−0.520836	+	0.853657i	$0.674380\pi$
$978$	−36.7015	−	22.4848i	−1.17358	−	0.718986i
$979$	26.6940			0.853144
$980$	−12.6396	−	6.02009i	−0.403756	−	0.192305i
$981$	−22.4987	+	19.4418i	−0.718330	+	0.620730i
$982$	−5.85838	+	48.3477i	−0.186949	+	1.54284i
$983$	−19.5897	+	33.9303i	−0.624814	+	1.08221i	0.363763	+	0.931492i	$0.381492\pi$
$983$	−19.5897	+	33.9303i	−0.624814	+	1.08221i	−0.988577	+	0.150718i	$0.951841\pi$
$984$	−5.82756	−	22.2311i	−0.185776	−	0.708701i
$985$	−12.5096	+	7.22239i	−0.398587	+	0.230125i
$986$	−2.88058	−	2.16350i	−0.0917364	−	0.0689000i
$987$	40.0451	+	40.6215i	1.27465	+	1.29300i
$988$	15.1130	+	52.0800i	0.480809	+	1.65689i
$989$	−20.7919	−	36.0125i	−0.661142	−	1.14513i
$990$	6.92501	−	14.1497i	0.220091	−	0.449706i
$991$	20.2495	−	35.0732i	0.643247	−	1.11414i	−0.341456	−	0.939898i	$-0.610920\pi$
$991$	20.2495	−	35.0732i	0.643247	−	1.11414i	0.984703	−	0.174239i	$-0.0557467\pi$
$992$	39.6229	−	18.8611i	1.25803	−	0.598842i
$993$	4.87561	−	10.6569i	0.154723	−	0.338187i
$994$	−22.1166	−	11.6282i	−0.701497	−	0.368825i
$995$	−18.2841			−0.579644
$996$	−17.5747	−	44.3936i	−0.556874	−	1.40667i
$997$	7.76394	−	13.4475i	0.245886	−	0.425888i	−0.716494	−	0.697593i	$-0.754254\pi$
$997$	7.76394	−	13.4475i	0.245886	−	0.425888i	0.962380	+	0.271705i	$0.0875877\pi$
$998$	−14.8857	−	34.9142i	−0.471199	−	1.10519i
$999$	0.204068	+	0.195373i	0.00645642	+	0.00618134i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.cf.a.101.60	yes	256
3.2	odd	2	inner	840.2.cf.a.101.69	yes	256
7.5	odd	6	inner	840.2.cf.a.341.112	yes	256
8.5	even	2	inner	840.2.cf.a.101.17	✓	256
21.5	even	6	inner	840.2.cf.a.341.17	yes	256
24.5	odd	2	inner	840.2.cf.a.101.112	yes	256
56.5	odd	6	inner	840.2.cf.a.341.69	yes	256
168.5	even	6	inner	840.2.cf.a.341.60	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.cf.a.101.17	✓	256	8.5	even	2	inner
840.2.cf.a.101.60	yes	256	1.1	even	1	trivial
840.2.cf.a.101.69	yes	256	3.2	odd	2	inner
840.2.cf.a.101.112	yes	256	24.5	odd	2	inner
840.2.cf.a.341.17	yes	256	21.5	even	6	inner
840.2.cf.a.341.60	yes	256	168.5	even	6	inner
840.2.cf.a.341.69	yes	256	56.5	odd	6	inner
840.2.cf.a.341.112	yes	256	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.cf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.170119 + 1.40394i) q^{2} +(1.41157 - 1.00373i) q^{3} +(-1.94212 - 0.477674i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.16905 + 2.15252i) q^{6} +(2.47291 + 0.940605i) q^{7} +(1.00102 - 2.64537i) q^{8} +(0.985054 - 2.83367i) q^{9} +(0.554645 + 1.30091i) q^{10} +(1.85655 - 3.21564i) q^{11} +(-3.22089 + 1.27509i) q^{12} -6.09443 q^{13} +(-1.74124 + 3.31181i) q^{14} +(0.720590 - 1.57504i) q^{15} +(3.54366 + 1.85540i) q^{16} +(1.02488 - 1.77515i) q^{17} +(3.81073 + 1.86502i) q^{18} +(2.22451 + 3.85297i) q^{19} +(-1.92076 + 0.557382i) q^{20} +(4.43479 - 1.15440i) q^{21} +(4.19875 + 3.15354i) q^{22} +(5.38747 - 3.11046i) q^{23} +(-1.24223 - 4.73887i) q^{24} +(0.500000 - 0.866025i) q^{25} +(1.03678 - 8.55624i) q^{26} +(-1.45376 - 4.98864i) q^{27} +(-4.35338 - 3.00801i) q^{28} -1.24278 q^{29} +(2.08868 + 1.27961i) q^{30} +(-6.71818 - 3.87874i) q^{31} +(-3.20772 + 4.65946i) q^{32} +(-0.606984 - 6.40258i) q^{33} +(2.31786 + 1.74086i) q^{34} +(2.61190 - 0.421865i) q^{35} +(-3.26666 + 5.03279i) q^{36} +(-0.0470857 + 0.0271850i) q^{37} +(-5.78778 + 2.46763i) q^{38} +(-8.60271 + 6.11716i) q^{39} +(-0.455776 - 2.79146i) q^{40} +4.69122 q^{41} +(0.866272 + 6.42258i) q^{42} -6.68450i q^{43} +(-5.14167 + 5.35834i) q^{44} +(-0.563752 - 2.94655i) q^{45} +(3.45040 + 8.09286i) q^{46} +(6.22372 + 10.7798i) q^{47} +(6.86443 - 0.937847i) q^{48} +(5.23052 + 4.65206i) q^{49} +(1.13079 + 0.849299i) q^{50} +(-0.335077 - 3.53445i) q^{51} +(11.8361 + 2.91115i) q^{52} +(1.35995 - 2.35551i) q^{53} +(7.25109 - 1.19234i) q^{54} -3.71310i q^{55} +(4.96367 - 5.60018i) q^{56} +(7.00739 + 3.20592i) q^{57} +(0.211419 - 1.74479i) q^{58} +(-6.29130 - 3.63228i) q^{59} +(-2.15183 + 2.71471i) q^{60} +(4.32809 + 7.49648i) q^{61} +(6.58842 - 8.77210i) q^{62} +(5.10131 - 6.08084i) q^{63} +(-5.99593 - 5.29612i) q^{64} +(-5.27793 + 3.04721i) q^{65} +(9.09212 + 0.237025i) q^{66} +(-3.73488 - 2.15633i) q^{67} +(-2.83839 + 2.95799i) q^{68} +(4.48273 - 9.79819i) q^{69} +(0.147942 + 3.73873i) q^{70} +6.67812i q^{71} +(-6.51003 - 5.44238i) q^{72} +(8.02450 + 4.63295i) q^{73} +(-0.0301560 - 0.0707304i) q^{74} +(-0.163471 - 1.72432i) q^{75} +(-2.47981 - 8.54551i) q^{76} +(7.61573 - 6.20570i) q^{77} +(-7.12467 - 13.1184i) q^{78} +(6.87818 + 11.9134i) q^{79} +(3.99660 - 0.165004i) q^{80} +(-7.05934 - 5.58263i) q^{81} +(-0.798064 + 6.58621i) q^{82} +13.7830i q^{83} +(-9.16432 + 0.123598i) q^{84} -2.04977i q^{85} +(9.38466 + 1.13716i) q^{86} +(-1.75426 + 1.24741i) q^{87} +(-6.64811 - 8.13018i) q^{88} +(3.59457 + 6.22597i) q^{89} +(4.23270 - 0.290213i) q^{90} +(-15.0709 - 5.73245i) q^{91} +(-11.9489 + 3.46743i) q^{92} +(-13.3764 + 1.26812i) q^{93} +(-16.1930 + 6.90391i) q^{94} +(3.85297 + 2.22451i) q^{95} +(0.148918 + 9.79683i) q^{96} -10.4589i q^{97} +(-7.42104 + 6.55196i) q^{98} +(-7.28326 - 8.42843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 30 q^{12} + 16 q^{16} - 10 q^{18} + 8 q^{22} + 128 q^{25} + 12 q^{28} - 40 q^{36} - 54 q^{42} + 16 q^{46} + 16 q^{49} + 36 q^{52} - 72 q^{54} - 16 q^{58} - 14 q^{60} + 80 q^{63} - 48 q^{64} - 60 q^{66}+ \cdots - 144 q^{96}+O(q^{100}) \) 256 * q + 30 * q^12 + 16 * q^16 - 10 * q^18 + 8 * q^22 + 128 * q^25 + 12 * q^28 - 40 * q^36 - 54 * q^42 + 16 * q^46 + 16 * q^49 + 36 * q^52 - 72 * q^54 - 16 * q^58 - 14 * q^60 + 80 * q^63 - 48 * q^64 - 60 * q^66 - 12 * q^70 - 50 * q^72 + 48 * q^73 - 16 * q^78 + 64 * q^79 - 8 * q^81 - 72 * q^82 - 56 * q^84 - 8 * q^88 - 72 * q^94 - 144 * q^96

Introduction

L-functions

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